Amp for B&W Matrix 803 S2

some thoughts
Your open doorway is a wild card and provides for bass leakage. The doorway makes for a bigger room as far as the speakers sound waves are concerned.
Only in this hobby can "leakage" be a good thing. I guess depending on who is hearing the leakage (wife?)

If you leave things as they are, one idea; you will get improvement by putting in a sliding curtain behind the speakers, in front of the TV. The curtain will open from the middle out to the ends. Close it to listen to 2 channel music covering the TV and providing damping for the speakers. Open up from the middle when the TV is in use - but leave closed behind the speakers. Also I can't see to the left of the sofa but treatment on that back wall with a panel or thick curtain will absorb bass waves; allowing you to be play music at higher spl levels and the sound will be better defined.

If your only limitation for speaker placement experiments is the AC outlets/wall modifications, and it is
1) not an apartment with landlord who doesn't want you making holes in the wall or
2) a wife acceptance thing; then I would experiment.

For one test you could borrow a thick 10 gauge extension cord for your amp/receiver and DAC and temporarily place speakers at both ends shooting down the room. This will allow you to experience the room effects with the speakers. You can then decide if it is worth it to you to modify the AC locations to accommodate this.

So finally my Luxman M600A is here. Sounds good especially for such price) Now it's time to think about preamp and DAC. The very first option is Luxman C600F and Aqua La Scala Mk II DAC...

Do yourself a favor and get a Pass Labs class A/B model. I have the x250.5 and it drives my Matrix 803 series II with aplomb. I've owned these speakers for 20 years (since they were new) and they sound the best with this amp. I also have the full class A 60 wpc model Aleph 5 and it just doesn't control the woofers as well as the class AB model does. If you are looking for something less expensive than Pass, I personally would take a long look at the Parasound Halo A21, which is also a high bias class AB design and could be considered a "poor man's" x250.5. Good luck and enjoy!