Thread necromancer!
After months of not trying to learn backwards circles I went out today and finally did some. What I figured out is elementary bike physics but learning how to apply it backwards felt like a big breakthrough. I am putting it here just in case it will be useful to someone (and also to show off).
Just like in a trackstand, in backwards circles you use pedal pressure to keep your bike in the same place underneath you, and you compensate for minor changes in body position by putting pressure on the cranks to move the bike likewise.
The difference is, instead of being directly underneath your centre of gravity your bike is a bit towards the direction your wheel is turned. The effect is that someone doing backwards circles is falling continually away from the direction their wheel is turned. If you start falling too fast (away from the direction your wheel is turned) you have to put more backwards pressure on the cranks to bring the bike back nearer your centre of gravity. If you start falling too slow, you have to put less backwards pressure on the cranks and let your body tip over some more.
That's it.