New Set Up

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.