Yeah, it took me a while to get it squared away in my head too. And then there's variations of Atmos speaker configurations to add to the confusion. You can have front and/or rear height locations, which are placed on the wall as close to the ceiling as possible. A combination of one or two of...
If you look a little closer at the SR7010 description you'll see that this avr can actually process 11 channels with 9 channels handled by the internal amps and the two additional channels managed by an external amp. So in your case you could do 7.1.2 without an external amp.
You need to get a 9.1 AVR. Don't know how much you can spend, but you should look for a 2014/2015 model if your budget is tight. I'm thinking a Denon X5200 or X7200 would work for you.