I also have trouble understanding why you use such a set-up. With 4 tower speakers and all the associated electronic devices, it must be awkward to walk around that room, as well as awkward to use them.
Why not use the
Onkyo TX-RZ 820 for both movies and 2 channel music? Its rated at 130 watts/channel, and the
Yamaha A-S801 is rated at 100 watts/channel. They are essentially similar to each other in power. I highly doubt if they generate audibly different sounds. Frankly, it's a myth that AVRs are good only for movies, and 2-channel receivers or integrated amps are better for music. An untrue myth.
What are your tower speakers? Do you have different speakers for movies and for music? Or are both pairs the same make and model? Why not use one pair of towers. You could sell the other pair.
If you simplify your arrangement, hooking up and using both sub woofers becomes rather simple.
There should be no problem with storing an integrated amp, or other electronic music or home theater devices. Remember to remove the batteries from the remote control.
Better yet, sell one of those Yamahas, or exchange it. If you simplify things, as I suggested above, you could sell both of them.