For what it's worth, since I'm no good at AH.
You won't get a barrel roll by holding the stick at a rear/side position. You will more likely get a roll into lawn dart type thingie. And the stall should be no surprise. Like an aileron roll, you must constantly adjust your control surfaces while the plane rolls. And I think full back deflection should result in a stall.
I don't understand why the split s does what you say. But I had a similar problem at one time. My game controllers didn't seem to work. I couldn't make any moves, other than a shallow bank turn, in any plane without getting the stall buzzer and a snap roll. Everyone was turning circles around me... literally. So I quit for a while. When I tried it again, all was much better. So, just for the hell of it, uninstall AH and remove/reinstall your game controllers. Calibrate your joystick in Windows and then reinstall AH. (You should have rebooted your PC at least once durig this.)
If you stick is too sensitive, tone it down by scaling and damping in AH setup. Remember, you must do this for each control surface separately and use the Apply Settings for each.
The only other thing I can think of is, don't force the planes to do anything. You should guide them instead. It's like there is a small delay when you move the stick. As the plane starts to respond, give it some more input. Like in the split s, your hand should be gradually pulling the stick back as your plane swings low and back up. Then relax it slowly rather than sudden, you will have less plane wobble that way. Don't force the stick, nudge it.
Happy skies,