Andrew, What kind of a system are you doing , 7.2? Multichannel class D amps are fine for the surround speakers. I would use amps like QSC PLX 3602 's for subwoofers (Class H) and I would use serious amps for the main speakers. These are all going to generate heat. Pass 600.8's or Parasound JC1+ would be fabulous. There is also Boulder and Constellation if you want to spend more money.
If you want to lower distortion further you want to cross to the subwoofers higher up no lower than 80 Hz using a high pass filter on the main amps.
One subwoofer will not do it. My guess is you will need four. You like the line sources because they project power. You can not use them well with a point source subwoofer. You have to create a line source subwoofer to match correctly. My guess is you will need at least 4 to create the array.
You can't put them in the wall but they can be positioned on the floor right against the front wall where they will be out of the way. Please check out the Trinnov processor
https://www.trinnov.com/altitude32/ This is a major cool unit and it has a great subwoofer crossover in it.
Please, what are some of your movies. I collect Blu Ray discs. I might have some already!