@erik_squires - yes, I do agree with all your points on multi-channel amps. It is, basically, a compromise to get 5 or 7 channels into a single device and still perform -somewhat- well.
The Monitor Audio speakers are 4 ohm, which will make it more difficult for an amplifier to drive. However, it doesn’t really drop down below 4 ohms like some speakers do, and most of the impedance is readily above 4 ohms:
http://www.stereophile.com/content/monitor-audio-platinum-pl200-loudspeaker-measurements#6kWsTrvo8jKsRcRR.97
That being said, you will probably lose some midbass punch where the impedance is almost a flat 4 ohms between 100 and 200 Hz. Also, some areas in the deep bass. The Classe amp is probably the best choice out of your 3 because of the "Class A" bias, but it is not really the best choice for the speakers.
Yes, nCore and ICE Class D amps can generate more power, but in my experience in research, the frequency response of Class D amps are typically dictated by the speakers impedance curve, meaning that the lower impedance areas will affect how powerful the Class D amp outputs. A Class D amp will probably perform very well on a speaker that is almost a flat 8ohms across the entire frequency range (much like a basic 8 ohm resistor). I don’t know about the newer Class D amps, but this is what I found with earlier Class D.
I don’t know if you are taking suggestions, but I have owned the B&K Reference 7 channel before. It’s more power than the Classe (at 200 w/ch). It has a Class A pre-driver and good power supply. The amp had really good power and volume and it was very sweet sounding, but I felt that the sound was too warm for me. At the time, I was running a Bryston SP2 Class A processor, so it was too much Class A in the audio path for me, but I think it could work out for you if you want to consider it.
https://www.audiogon.com/listings/multi-ch-b-k-components-reference-200-7-s2-7-channel-power-amplifier-9286-2016-09-20-amplifiers-80020-broomfield-co
Otherwise, another suggestion is to start buying up used Emotiva XPA-1L monoblock amps and run them in the Class A mode (30 watts). They are typically less than $400 each used, so it is in your budget. The only problem is supplying a separate outlet (or heavy power strip) for each amp. You need space for 5-7 individual amps and they do get hot in Class A - so you will need a good 3" space above for heat ventilation.