It sounds like your 3rd zone could have separate amplification, in which case you can use a 2-channel integrated amp with subwoofer out, like the
Marantz 40n, which has HEOS support, but that's $2500 US.
If you go with the 7015 AVR, I looked at the manual and to power 3 zones in stereo you can do 5.1 surround at best plus 2 powered stereo zones. If you want 7.2 in zone 1, then you can only power one other zone and run line level out from zone 3 preout to another amplifier. Couple options there. Use the zone 2 amps to drive the speakers in the other room and get a simple 2-channel amp to drive the ceiling speakers via zone 3 line out. The 2-channel amp can sit with the AVR. Other option is to use the zone 2 amp to drive the ceiling speakers and run the zone 3 line level out to the other room and add a separate amp there. You don't want too long of a cable run to avoid the cable picking up RF interference.
If you use the zone 2 or 3 amps for the other room, I would not worry about using the speaker level signal to drive a subwoofer. The sub uses a line level signal so draws a negligible amount of power from the speaker cables. It will not degrade the sound in any way. Same case if you use an amp with no subwoofer out. Just use the speaker cables and the speaker-in on the sub. The down side is that your speakers will get a full range signal, so you may have to cross the sub low to avoid too much mid-bass. Sub integration can be more difficult with the overlap in frequency response.
If you go for example the 40n route with subwoofer out, then you can high pass the main speakers like in most home theatre setups. It's the more expensive option but is more flexible. You'll need a separate amp for the other room any way, so compare the cost of using a straight amp to that of using a HEOS integrated amp like the 40n and see what fits your budget.