RE: Why does roll rate increase when inverted?
When you're upside down with a Skylane the airfoi now had a negative camber value. With such an airfoil the likelyhood of the airfoil stalling and inducing a snap roll condition is quite likely. Not to mention that you just turned a fairly extreme highwing design into a fairly extreme low wing design. Add all these together and we have potatoe salad.
Your Skylane shows this trait but it's due to a fairly unique set of charactaristics. Try flying a funfly or 3D model and it can't tell the difference from wheels up to wheels down and responds exactly the same either way.