Just passing through so a very short, incomplete response.When I do a flat upright spin in something like a Pitts - outspin aileron to flatten it, a lot of power to further flatten it then move the stick forward to accelerate it and flatter still.
Power effects include gyroscopic forces as well as direct thrust and slipstream so the effects are different between left and right spins.
Perhaps I will find a link for some reading on the subject.