2ch Upgrade for Unfocused Listening

I'm not much of a talker on this forum so forgive me for my rash introduction. I'm a father of two young boys, loves music and has little time to really focus on listening. That said, I am toying with the idea of upgrading my system to something a little more grown up. Current setup is a super modest, running a NAD D3020, pair of B&W bookshelves (10 years old), and a small Martin Logan sub. This system sits in the living room and is predominantly used for background listening though the occasional "sit back and relax" kind of listening does happen from time to time. If I'm not listening here, I'm at my desk working and listening to a pair of KEF x300a's. 

My big thought is to do a full upgrade, albeit a slow one, to something a little more special. Currently I have my sights on the Naim Uniti Atom and a pair of floorstanders (CM10 S2 really catch my ear), taking away the need for the ML sub. The big question is this however, will an upgrade like this where music is played more often than not when I am running around with the kids be something I notice? We all like to listen to music, but if we arent planted in the sweet spot am I wasting my time thinking we can achieve great sound throughout the space, making for a worthy investment at this current life stage. 

I welcome your input. And thank you greatly in advance. 
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bgrimes, does a table radio sound as good as your current system with indirect listening? If it doesn't you have your answer. I would say about 1/2 of my listening at home is indirect. I would sorely miss the kick of extended bass and a mid range that doesn't have a bite to it even when I am chopping basil for pesto. Actually, I think I chop in rhythm!
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" . . if we aren’t planted in the sweet spot am I wasting my time . . "
For critical listening, yes. For casual listening, no.

Omni-directional speakers should be considered as an option for the scenario that you’re describing. They excel at evenly radiating music around a room. Still, they should be placed out from the wall to breathe properly.

Or another possibility is to set-up satellite speakers around the room. Some AV Receivers/Processors allow the stereo signal to be distributed to all speakers evenly. (It’s not called surround-sound). This option allows the music to envelope the entire room. Denon used to have it. Don’t know about NAIM.

" . . floorstanders, taking away the need for the ML sub."
Floorstanders don’t automatically guarantee good bass. Much depends on how the bass waves bounce around the room and where the listener is located in the room. (Bass waves can be upwards of 20-30ft long). If anything, being out of the sweet spot would require more subwoofers (via a distributed bass array), not less. Though, sometimes, you can get lucky. While prepping in the kitchen, it’s very possible that the sound coherently integrates where you’re standing. Happily, this is true in my kitchen.

Of course, this is all subjective as to what works for you. Stick to a reasonable budget. Spend more quality time with your family than this crazy, expensive hobby.
For the big sweet spot essentially the whole room perhaps consider these.

It is noticeable and possible.
Having a Space that is 2-3 times longer than wide would help with one possibility.
Speaker selection / recommendation might prove difficult.
An example would be: Two Way vs Three Way Designs.
MBL 126 omnis should give you an idea of what is possible.
I would suggest listening.
Demos / Shows
Find a sound in a playback system that has a / the desired quality.
Already you have some reference with  CM10 S2.
Start with a component that you like!
The current Book shelve Speakers may serve well for some experimentation. 

What are your room dimensions?
Thanks for the feedback, clearly lots to think about. I have been curious about the Ohm Walsh speakers in the past and they continue to look appealing, but I dont like the idea of having whatever speakers I end up with pulled away from the wall. Right now, the kids get first priority when it comes to this space and the less intrusive this system can be the better. I also want to do my best to protect the investment, ie keep this stuff out of the kids' way.

Room size is a tricky one, what I would call the living room is 15.5' square, but it floods into the kitchen and had a vaulted ceiling. Below is an image link so you can see the space. (It's a mess, try to look past that. I've been on dad duty this week). 

One other item of note. We live in the sticks, literally 4hrs from a major metropolitan area (Denver), making demoing/listening not exactly practical. 

Other speakers I've only read about that I would consider are the following:
Tekton Lore
Buchardt S400 (used to be more excited about this one)
Devore Fidelity Gibbon X (or similar if I can get my hands on a used pair)

I would love to keep the speaker side of the purchase under $2k.

                Is there something about your current system that you don't like,or is it that itch that we all get?
Ah ... you are in the neighborhood ... Metropolitan Denver!
The Living / Kitchen / Listening Space is great!
Set up the B&W's opposite from the kitchen Area Space.
This should allow for some well deserved casual ... um ... critical listening.
Wall to Wall Boundry to Boundry.
You may have to move the mains out into the space a bit for the proper effect.
Experiment with spacing between the speakers as well.
The Sound just depends on how the loudspeaker integrates. 
Even without treatment you should be able to have a good idea of what the sound can be.
Lots of possibilities for brand set of Loudspeakers.
Don't look now ... but TMR Audio is listing a Clearwave Symphonia 1
used but Not ... for a bit more than $2K.
Do look!

You might consider Morrison Audio.  Extremely well thought-out design.
TMRAudio listing does show that the item has had Two previous owners
assuming ’use’ at One year. Same Serial No though.
A bit of confussion.
TMRAudio had a 2018 listing noting unused.
Oh well.

rocray: To answer your question, I would say it's a little of the itch, but also about experience more out of my music. Though oftentimes music takes the background in my house (unless I am working at my desk), I like to think I can get more of any experience out of music while playing in the living room with the family. I know the power music has on one's soul and I want to find a little more of that for myself while letting my kids experience it too. There are a lot of moments when I tell me myself, what I have is just fine, but then there is this deeper urge to hear more. For example, I wouldn't say anything about my system now excels in clarity or definition of the music. Right now, the sound being created doesn't get inside of you; you hear it, but you don't feel it (and I'm not talking low-end bass) if that makes sense. I want it to excite me and rediscover what I loved about music in the days of my youth when I would go to shows weekly and spin records with friends. 

rego: Thank you for your comments. Lots to think about there. Are you in the Denver area? I have thought about placing the current speakers on the far wall but always come back to the fact that I wouldn't be able to run wires in a clean way with the fireplace sitting in the middle. Those TMRAudio speakers, do look nice, though a little high for my budget and the chunk out of the corner gets to me. When you look at a speaker like this, what specifically jumps out at you when it comes to my situation? 

Omni-directional: It really is raising an eyebrow. The fact that there have been several suggestions to go omin-directional does get me thinking. Most suggestions are WAY out of my league, but Ohm has something I should be paying attention to. The continued suggestion does lead me to think a more traditional 2- or 3-way 2ch setup will never be a suitable solution in creating good/decent sound if I am not sitting in front of it. There is part of me that says, "wow that's crazy," but another part of me that really gets where that is coming from, though still crazy.
@bgrimes I have a similar sized family room and a very big and strong 3 year old toddler. So I have the same concerns as you on putting a speaker system where the kid plays.

My boy has become more mature and will likely not break the drivers anymore, unlike when we was around 2 years old.

So I was looking at a speaker to provide the following:

1) a large sweet spot
2) a heavy speaker that is not easy to knock down
3) driver made with safe materials (non toxic)
4) speaker can be placed 1-2 feet away from the back wall
5) drivers that are strong and difficult to break with little fingers
6) a speaker I know will take abuse and get scratched up (so less pricey the better)

With these criteria I am thinking something from ELAC or KEF R series. I like the coincident drivers and feel they give you a bigger sweet spot. There are others with bigger and better individual aspects of what I described but I am taking everything into consideration.

Buying used on A'gon will also get you near the $2K range you want.
"Then there is this deeper urge to hear more" I totally get that. I think that is the driving force in this hobby. Very well put. 
   I also agree with exposing your kids to well presented music. While growing up,there was almost always music playing. My folks never had anything that resembled a "hi fi", but the music was there. This is what got me started in the pursuit of better sound. ( For better,or worse!)
"Omni-directional: It really is raising an eyebrow. The fact that there have been several suggestions to go omni-directional does get me thinking." 

Imo the argument for a quasi- omnidirectional system in your situation is this:  

Good timbre largely comes from a) the first-arrival sound being spectrally correct and b) the reverberant sound also being spectrally correct.   So an omni system has the basic characteristics you need to get enjoyable timbre pretty much throughout the room.  Yeah it would be nice if they can be positioned well out in the room away from the walls, but they won't suck if that's not possible.   By way of analogy consider this:  An unamplified acoustic guitar sounds good from every direction (kinda like an omni), and it doesn't suddenly suck if the player is up against the wall. 

Ohm speakers are designed to work close to walls. If I'm not mistaken I believe a mere foot from the wall is even recommended by Mr. Strohbeen. I had my MicroWalsh Talls this way for years and they sounded wonderful. If memory serves, the reason they work so well close to walls is they are psuedo-omni:


A nice feature for those with kids .. the drivers are housed in a metal can so those little fingers can't poke them. 
The pairing of B&W monitors and a  Martin Logan subwoofer is perfect.IMO, step up to a pair of B&W 805 monitors and improve upon the electronics as desired. This will give you options to sit in the sweet spot or listen on the run.  Keep us posted on this development. Have fun!
Happy Listening!
@jafant Very interesting idea. I've actually eyed the CM6 S2's as an option in this same kind of subwoofer-needed configuration. I'm guessing there is no comparison between the two, but how would place the CM6 S2 next to 805 monitors? I will sometimes waver between truly full-range towers vs monitors and sub with this idea that a single package, i.e. a tower producing all frequencies would produce a more harmonious sound. Thoughts?
@audiokinesis  Thanks for posting about Morrison Audio.  The MBL 101E has been my dream speaker for many, many years.  Luxuriantly, 3D.  Unfortunately, it's way above my pay grade.  The Morrison Model 29 seems within striking distance.   I need to find out if they have representation in L.A.      OP: apologies for going off-topic.
Revels and Magico are among speakers I find to have very wide dispersion and therefore best for listening from a wide variety of locations.

Aurora, Co.

Three Way Designs have consistently Sounded better to me.Mostly that the Listed Price @ $2645 is close to your specified Range.The thing about used gear is having cash on hand when it comes up.

Though I think 2x Designs have improved signicicantly … say in the last ten years.

Improved time alignment driver motor structure X-over … a combination of these and more.

The Symphonia 1 listing notes a 'Coherent Point Source Mid' / 'X-over improvement'.

Also "Bass and Imaging is Outstanding".

Call / Email TMRA and ask for someone to give more input!

Good Staff.

In short a Good well Implemented design for $2.6K.

You can get a Book-Shelf to keep the setup on the periphery.

And You Are Welcome!