Thanks for the (quick) suggestion.
I have 3 rooms, 8 ohms R & L in each, for 6 channels in addition to the 5.1 in my living room. The volume controls in each room can take 100W RMS. Likewise, the speakers can handle 100W RMS / 200W peak. The 105W RMS / 215W peak from my Denon AVR-2313CI has been a good match - I've been able to test one pair of speakers at a time with my zone 2 speaker outputs. I planned to keep using those zone 2 outputs for 1 room and use the new amplifier for the other 2 rooms, so I need 4 more channels.
I did look at the AudioSource series in my search. All of the AMP's are 2-channel models except the 1200 (12 channels). The best option might be one AMP 310 ($458, 225W into 4 ohms) with speakers in parallel getting 112.5W each. Alternately I'd need two AMP 210's ($348 each, 90W RMS into 8 ohms). There's a chance two of the AMP110's ($280 each, 75W per channel) would be good enough. The AudioSource info does indicate 12V trigger.
The Pyle is still tripping my Denon receiver whenever the Pyle powers off and is connected via RCA's to the Denon. That worries me, both for damaging the Denon and for not being able to add an external 12V-controlled relay.
I measured the quiescent current on the Pyle's AC supply to be 200 mA. At 11.7 cents per KW-Hr, I'm looking at $24/year to leave it on all the time. But then I have to worry about it...just in general given what I've already seen and the negative comments.