Yes you can use Drag and Drop. But it has it's own pitfalls. however personally I think it's cleaner.
1. Make sure the D&D object always stays at the root of the object list. Putting the DD in a folder will break the system.
2. You need to work on fixing the offset of the D&D object. A D&D object doesn't center to the location of the touch. The D&D offset is where the touch occured.
3. D&D that is currently being dragged doesn't like having the .setPosition used to recenter to the touch position.
4. Ashley doesn't suggest using the D&D object for input control. Not sure why I thought the use of it was slick. But as mentioned in 1,2,3 it can break the system and there will be no BUG fix for it.
As for you to fix your current problem due to angle. That's because there is no built in dead zone. So even the slightese off center will cause the other direction to trigger. Now if you can pixel perfect control then no problem. So I don't do that.
deadzone = 10
fangStick.x > fangPad.X
fangStick.x > fangPad.X + deadzone
fangStick.x < fangPad.X - deadzone
alternativly you can instead check against
fangStick.XP > 10 then simulate right
fangStick.XP < -10 then simulate left