> It goes without saying, but have you gone into the MAME controls menu (which is not > the in-game settings but is accessed by default TAB key), and adjust analog > sensitivity?
Yes. If I have it on the lowest setting it doesn't really move the slider at all. The higher I move the sensitivity the more I can slightly move it before it snaps back. Even on the highest setting (255) it will move a few pixels and go back to the left immediately.