What is the right choice?

So I am looking to upgrade from a NAD C356BEE integrated receiver to something that provides better sonic fidelity and a phono connection and onboard DAC. The budget/price point is around $1000 to $1600. So far two different sale people recommend the Yamaha s801. I have also listened to the NAD c368 and c388 with my speakers attached which I have brought to the local dealer for demo.

So I look for reviews and come across Sean from Zero Fidelity who provides an interesting approach for a technology review of audio gear. He conveys a comprehensive look at the technology piece inside and out and leaves you with a pretty thorough understanding of how the Yamaha s801 will sound. A good performing piece just not great. Sean then leaves you with a look at some comparable amps.  The NAD c316BEE and the IOTAVX. The NAD is not worth mentioning relative to this study but the IOTAVX Stack based on all of his reviews is what I should be looking at.

Can anyone share their experience with IOTA's technology and service?

Is this the right step up in fidelity from the NAD c356?

Should I be looking at Arcam, Cambridge, Marantz, Pro-ject and Quad as part of this study? 
What speakers?  Digital tech moves so quickly I'd be looking at a Rega Brio and pick an external DAC of your choice if it'll drive your speakers well.

I've heard the Yamaha it's a great sounding amp the DAC is definitely the bottleneck but it still sounds quite good.  Marantz also has a couple models that are supposed to be quite good not sure if they include a DAC or not.

I currently have a pair of PSB Imagine B's which I am upgrading to the PSB Tower T2's.
I own a Yamaha A-S701 and the NAD 356BEE. Though the A-s801 has a different DAC than the A-S701 I believe the pre/amp stages to be the same. I don't believe the A-S801 to be an upgrade from the NAD356, rather a more lateral move with sonic differences. The NAD sounds warmer, the Yamaha somewhat brighter with somewhat greater resolution in midrange. Which integrated would pair best with the PSBs is subjective.  Advantages with the A-S801 are the internal DAC, phonostage, headphone output, subwoofer out. 
Parasound also makes a great integrated with the features you are looking should be able to find used in your price range. Tough to beat a John Curl design.
   I can't speak about other brands of equipment mentioned here but I can speak about NAD and PSB. When I sought to upgrade my system and went with a NAD amp (C375BEE). I used the amp with an existing pair of Klipsch speakers (their top of the line Reference series). The sound was just OK but I didn't think the speakers were doing justice to the amp. Went back to the dealer and heard the amp thru some PSB speakers. What a difference!
   The 375 came with available ports to install a phono and/or a DAC module. I opted for the phono module. Sounded OK but have since employed an outboard phono preamp. It was an improvement. Don't know how the DAC module would sound since my preference is mostly vinyl and CD's.

   The C375BEE I have is an earlier generation than the 388 series. It is analog rather than digital. Funny thing about these amps that you can never look just as power output. When I compared the C326BEE sounded much better musically than the C356BEE with more power. The 375 brought back the musicality of the 326. But neither with the Bluetooth and streaming capabilities of current models.

   So, it all comes down to personal preference of sound and room acoustics. Those who say NAD has a "warm" sound do not have much experience with NAD. My current system is the C375BEE, a pair of PSB Imagine B's and two subs. Good luck in your hunting.

love my Parasound Halo integrated, you could find one for $1500 if you are lucky...
And speaking of Parasound, they have their new NewClassic 200 Integrated which looks very promising for $1,200. 110 watt Pascal class D power, Burr Brown dac, bass management, HT passthrough (including subs....I think), MM/MC phono. Pretty much everything you can ask for all in a nice small 1U package. If this sounds as good as their Z Custom line of products which I own for a second system, this may be hard to beat.
I like the Parasound integrated idea.  You should be able to buy that for $2,500 with some negotiating.  Last year at the RMAF, they sold 3 for $2,250.  Parasound puts out a lot of current.  Not sure why manufacturers talk about watts when they should talk about amps.
I believe what constitutes 'warmth' is subjective. I have owned several NAD amplifiers throughout the years and have listened to several others. I would not declare them to be, as a class, warm, however in comparison to the A-S701 it seemed to me that the NAD 356 was more so. I might have declared the 701 as more airy, lighter. Since warmth has much to do with the speakers in use, I should add that this comparison was made with a pair of B&W CM5s. 

I also owned the NAD 326BEE prior to the NAD 356BEE, made the change because I was using them in a secondary system for outside use and the slight extra power (headroom?) provided by the 356 proved beneficial. Other wise I would have kept the 326.  I agree with jrpnde that is was 'more musical'.

I have also listened to and enjoyed PSB speakers, most recently Synchrony 1s. And have heard that NAD mates well with PSBs. I have not heard then together however. I do believe NAD provides the amplifiers for PSB subwoofers. 

At the moment, if I was considering the purchase of a new integrated having both phonostage and DAC, at a budget limit of $1600, I am not sure what I would purchase. If wanting to stay closer to $1000 budget and purchase a new product, I would consider the A-S801 or the Outlaw receiver (forgot model). There are likely more contenders.  That said, I would most likely look at purchasing a used recent model integrated which retailed at ~$2500 for somewhere between the aforementioned price points with the features required. 
   mesch...There has been a bit of discussion on this thread about the combination of NAD amps and PSB speakers. I am quite curious about your comment about what you heard with the PSB Synchronys. Before the Imagine line came out the Synchrony line was supposedly the flagship of PSB. I have read a lot of reviews and opinions comparing the two different models and seems that most opinions favor the Synchrony over the Imagine. Since the Synchrony series has been out of production for a while, the only option is in the used market. I just wonder how much they are superior.
   I am using a pair of Imagine B's with a pair of two 10" subs. I would like to stay with the use of the subs so stand mounts would be preferable over floors standers. So, the option would be the Synchrony 1B. The Synchrony 2B is also out there but just a peg down from the 1B. Obviously, auditioning these speakers at a dealer is out and I am wondering if you or any of the others posting on this forum may have first hand experience with comparisons of the two lines.

I appreciate all the feedback I received from this post, however I have not had any comments on the IOTAVX S3/P3 possible decision. This would be an upgrade to support the need for a phono input, a DAC and some additional wattage. Does anybody have experience with this brand?
Now I am adding an additional question relative to another one of Zero Fidelity's high ranking reviews, the Buchardt S400 bookshelf speaker.

Does this pairing makes Hi-Fi sense? IotaVX and the S400? Is this a sonic upgrade from the NAD C356 and the PSB Imagine B's?

Sean from Zero Fidelity, care to comment?
Jrpnde, yes at the time I heard the Synchrony 1s they were the PSB flagship speakers. I did not hear then with NAD amplification. They were driven by a Rouge Chronous Magnum.  I can't comment regarding comparison with the Imagine series.