My only addition to what's been said would be to decide what you need based on actual and preferred SPL. As I used myself as an example (my desire to be able to clear Reference Level Dynamic Peaks and have those 5 channels matched as closely as possible), it seems only fair I continue.
I know that at 85dB sensitivity, I only need 1w @ 1m to achieve Reference Level SPL, but the 20 dB peak will require ~128w @1m. I sit about 8' away in a small room, ~11x15', ~2000'3. Due to the size of the room, I likely do not experience the 6dB drop upon doubling distance, rather probably -3dB. Accounting for that, I would still need to double my power from 128w to 256w, achieving 109dB @ 1m... adjusted should yield ~106dB @ 2m.
Looking at your room, you would clear 105dB @ 1m with 32w. Assuming a large room with little boundary reinforcement, 2m would have you drop to 99dB, and 93dB some 12' away. Again, I stress the assumption being made that you have no support from boundary gain. If you do and on the otherhand, and only experience a -3dB drop per doubling of distance, then you only require 128 watts to get that Reference level Dynamic Peak at a LP 12' away.
Our favorite tool to recommend is this online
SPL calculator. It takes many more things into account than I can.
Either way, I would consider looking for a strong 3-channel amp to handle the Front-3 over a 7-channel Amp. If anything, I might consider putting the surrounds on a different Amp altogether, over time. However, your AVR is strong enough to handle 4 surrounds quite well. If you want to future proof against adding more speakers and needing stronger and more amplification, maybe consider a 5-channel amp and include your L/R Surrounds, leaving your Rears on the AVR amp.
Mind, this is just an exercise.
I did this to myself, too, before deciding on my Monoblocks. Regardless, It comes back to one thing: Your Ears, Your System, Your Ducats!
I am not the guy to say you don't need an amp. I ask instead: is a 7-channel behemoth the right path?
Cheers!