Home Theater Receiver recommendations for B&W 803S?

Interesting.  Sorry, I do not have any direct experience with the Monolith products.  It's a full linear power supply where the Emotiva is switching power supply.  I do have much experience with Emotiva amps, having had several over the years.  Up to you, but I would probably spend more on the Emotiva because of XLR balanced inputs and that I know it has pretty good amp boards.  Good luck on your testing.

The newer versions of the Monolith actually do have balanced inputs.

And hey, for what it's worth, someone left this review on the Monoprice site:
"I have a Monolith 5 and an Emotiva XPA-5 Gen 3 ... I prefer the sound of the Monolith ... It sounds more rich, detailed & powerful."

I'm willing to spend a little more if it sounds better - but at this point I'm kind of playing a guessing game, unless I can find a way to demo both (and Rotel...!).

Agree with auxinput on the Rotel RMB-1585 amp. You should definitely grab that used Rotel RMB-1585 five-channel power amp on Audiogon for $2099. New retail price is $3k. I highly recommend this amp. My buddy has this amp in his home theater room driving the B&W 804 D3 speaker system. Very refined very musical with smooth highs and rich tonal and natural mid-range bloom and bottom end grunt. The sound was fluif, liquid, effortless and very analog. Highly recommended! This amp is very well built and has lots of power reserve to drive just about any demanding speakers effortlessly. This amp is huge massive and very heavy weighing in around 81 lbs. Do not hesitate to buy this amp.

The Rotel will sound very goon on the B&W. They usually have good synergy together. 

I heard Rotel at RMAF and I will have to say that it is a very nice and refined amplifier.  Obviously, it's not going to be in the higher priced "Krell" or "Parasound" league, but it is extremely good and much better than Emotiva (I have actually owned three different models of Emotiva monoblocks).  That review on Monoprice could have some element of truth to it because the current generation of Emotiva uses switching power supply, which doesn't always have a lot of bass authority.  The linear power supply of the Monolith could be transferring the bass power a lot better.  But the Rotel will sound much better than either.  Over the years and testing with different equipment, I have found that, in the end, you really get what you pay for.  Of course, there are many variations of sonic signature, but if you are looking for sound quality and refinement, there are no real cheap shortcuts.  The Emotiva will have good sound for the money, and the Monoloth may have good for the money as well, but realize that you are making compromises here.  If, ultimately, your budget cannot do the Rotel, then that's perfectly okay.  Just keep a realistic picture of what you're getting.

You two are making a pretty compelling case for the Rotel!  

However I just took a measuring tape to my cabinet, and I don't think I can actually get it to fit along with my Denon (or the Marantz). The Rotel is really huge... The Monolith is about 2" shorter. So that may win the argument.

Then again, it may be time to go rack shopping...  Rabbit hole, indeed...