New Set Up

Starting fresh in a small fire place room 3.35m x 3.35m. Speakers require near wall corner placement. Plan to use Roon, Tidal, Quobuz. Have demoed a range of equipment. Considering: Kii3 and Trinnov Amethyst, Naim Uniti Nova and Wilson Tune Tots, Naim Uniti Nova with Jern 14EH (I prefer not to have a sub-woofer), Audio Note Cobra with AN-K/SPe (have not been able to demo, however have read speaker placement and product quality, Leben CS600X, Chord Hugo 2, Chord Hugo M Scaler, Trenner & Friedl Sun or Osiris and Naim. Secondarily, I'd like multi-room audio capability for kitchen etc. Upon initial listening I've been impressed with performance of the Leben with T&F. It sounded open, a substantial soundstage and smooth/rich sound.  I've had an LFD LE VI amp with Harbeth p3esr speakers. I realize this is quite general, however I'd appreciate any guidance or sharing of experience with any of these systems. Thank you
Speakers agains a wall require speakers that are no dipoles.
You post has a lot of aspects.I would separate them.

The challenging room and speakers are probably the most important.
As budget usually comes in at some point, what is it?
My total budget is about 27k. I have a sense of the room challenge. It's the reason for identying the AN-K SPe speakers and also considering the Kii3. Your guidance is appreciated.
I have no experience with either of those speakers and see no measured data for them, so I can offer no suggestions other than my opinion that the speakers are THE most important part of the system.
Many claim that the room itself is the most important.

On the electronics and source side, things like MiniDSP, the TDAI 1140, etc. I also have no experience with. However they seem like they could be useful for helping the room… at least in theory. And hence I am mentioning them.
Some of those smaller speakers have a lack of bass, so the addition of a small powered sub might have a role… provided that they actually have some output below where the speakers peters out?
I am scheduled, next week, to listen to the ATC SCM20, Spendor 1/2 and Dynaudio Confidence 20 with Naim Uniti Nova.  What are your experience and thoughts on these? I'd appreciate your suggestions for things should be mindful of during this type of demo.
I have 35 year old speakers, and while I have a new second hand amplifier, my preamp is also last millennium (‘98).
All I know for sure is that it took me ages listening to speakers, and I also had a guiding hand helping (slapping) me out. That also applied to the preamp and amp from that era.
Literally it took months of looking and listening.

The fact that they still seems to work is somewhat of a testament to things, but the specific speakers are well known to not work in a corner. 
I would recommend you make a list of dipole, bipole and monopole, and listen to examples in each group. Dipoles are known to work in small room, but not in the actual corner. If you find examples of each that you like, then it gets down to whether you can try them in your room. (Most bookshelf ones are monopole, maybe with a rear port… I like how the dipoles work myself)
Starting that way you at least could separate out di/bi/mono, which maybe help to sort through the chaff?
That Naim seems a lot like the TDAI 1120 or TDAI 3400. Just that the later two also have a room correction built in. Either you are a purist that wants none of that, or you can appreciate it.
I have both, so I guess I may become a fence sitter? The HT one is actually in transit, and it has the room correction, and then I can either push out of it, or out of the 2.1 in purist mode.Hence my only suggestion is that I suggest that you listen… Not that room correction is required or recommended… just that most higher end systems do have some correction and leveling in the <200 Hz region.
There are a couple of Lyngdorf dealers in Beijing, so I would be interested in you perceptions of the TDAI versus the Naim unit?At least it can be fun looking… better bring some CDs you know and like.
Spotted the reference to ATC SCM 20.  I would simply add active to that already great ATC speaker.
Spotted the reference to ATC SCM 20.  I would simply add active to that already great ATC speaker.
I know nothing about the ATCs either, but if they are like a Dutch-n-Dutch, then it opens up opportunity when they just get an input signal.
Yesterday I listened to ATC SCM20, Dynaudio Confidence 20 and Spendor Classic 1/2. All with the Naim Nova. Streaming Tidal and Quobuz with Roon. My preference was toward the ATC. It seemed closest to a live experience. I felt there was a lot of detail. I'm going to set up a second  Kii3 demo. I'm also working on setting up a demo for Audio Note AN-K and Cobra integrated Amp. I'm trying to be thorough in the decision making process. I'm also trying to hear the Gold Note IS-1000 Deluxe but it's difficult finding a dealer and getting a demo.
I have Dynaudio C2's in my main system and love them and have an old pair of merlins (with Dynaudio tweeters) which I'm still using as well.  . Not as fond of the new Confidences, but others love them.  A matter of taste, not quality of sound.  On the other hand, in my smaller system which is in a room similar to yours,  I'm running a Nova with Neat Iota Alphas and am getting spectacular results.  Am considering a sub to give it a little more body, but could live forever with the Nova Neat combo as is.  The speakers are small, but give shockingly big/good sound.  It would be worthwhile looking at the Iota Alphas but if you want/need more, I'm guessing the larger Neats might be interesting. Someone with more experience with Neats might have thoughts on their power needs.  Not saying the Neats are the answer, but they should certainly be explored.
I appreciate your suggestion. I'll find a local dealer where I can check out the Neats. What speaker cables do you use?
What speaker cables do you use?
Literally lampshade wire at the moment.

But usually I use Mogami, however I am going to try some Kimber 12TC as they are the lowest inductance that I know of.

When the new cable comes in I will remove the lampshade (temporary) cables that I needed to use when going from dual mono blocks to a stereo amp.
OMG what a horror show! OP you are taking advice on a $27k system from a guy literally using lamp cord, who buys based on inductance because he thinks it all sounds the same anyway. Sorry. This happens. Nothing we can do about it. Free forum, anyone no matter how .... nevermind.    

I will let you in on a little not-secret. I have never once in my life come here asking anyone for advice, and for precisely the reason you see above. It is a crap shoot, and odds are that is what you get, crap. Lamp cord. Holy freaking..... lamp cord.

I rest my case.

Search bar. Search function. Lamp cord. Sheesh.
But they are high quality lamp cords with cryogenically aligned copper, and fairy dust.
Great @holmz bet it sounds electric, en-lightning, so do you have incandescent or led crossovers?
Yes, you get advice here, but you have to be very discriminating in what you believe.

Given your question, I would start with The Absolute Sounds’ and Strereophiles Recommended Products issues. Look at stuff at or above your price range… you can always drop a couple tiers in a company compatible with your aesthetic. 

Do components first. So, lamp cord is compatible with the first pass, getting your components the best you ca possibly afford. Then phase two is work on getting the best (for your system) speaker cable, interconnects… maybe save up some more money while enjoying your system and then go for a power conditioner and power cords. Take your time and you will likely be really happy with your system. Cables, interconnects tend to be most cost effective in the 15% range… plus or minus depending on the system.
@jerryg123 just 1st order cross overs… and passive.

Regarding the Neats, I have no idea. But there are also speakers like the Dutch-n-Dutch which are powered. And if a powered speaker was chosen then they do not even require a speaker cable.

Whether an amplifier with room correction is used or not also adds some decisions… and these days there is a lot of options that can be used to fix up a room digitally. But the purist approach is often preferred. 

There are so many options, that it should be expected to be a complex process to come up with what is optimal. Which can make it a bit of fun… or daunting.

Again, starting with the speakers are working backwards is a sensible way to approach it. Or if one wants the room correction, then know what a particular amplifier can drive, can also influence the speaker choice… so it can be complex.

I read no mention of acoustic treatments. You 

have a difficult room and if that hasn't been addressed 

yet, that is the first priority.

OMG what a horror show! OP you are taking advice on a $27k system from a guy literally using lamp cord, who buys based on inductance because he thinks it all sounds the same anyway. Sorry. This happens. Nothing we can do about it. Free forum, anyone no matter how .... nevermind.     

If he gets the Kii-3 then he only needs the lamp cord for running power to speakers ;)
(No external amps, no speaker cables.)

That would not be a bad choice for speakers, and their review just came out a few days ago.

Dutch-n-Dutch also come to mind.

Be wary of speakers that impress you with "detail" on first listening, as they can become fatiguing over time.  I'm not saying always, but be careful. I find a good test is to play something off Brubeck's "Take Five" record and listen to Paul Desmond's alto sax at a normal listening volume.  If it sounds harsh or in your face, run. That alto falls right into the "annoying" range of frequencies IMO.  People spend a lot of money on "detailed" systems and thousands more trying to back it off with cables, footers, fuses and whatever. 

Thank you for the suggestions. Most recently I listened to Wilson SabrinaX,BAT80i, dCS Bartok. I listened to a fairly wide range of music from various eras. I found the the system to be natural, detailed, well balanced. It was easy to listen. Not to forward or "in your face" in any way. There was good bass without booming in any way. The room had no special treatments. Right now I may be reconfiguring my primary  listening space so I'm continuing to explore options.