I know you posted this a while ago, but recent software updates have made it so that it's kinda possible to adjust the deadzone:
Before this last update, whenever I held the stick in one direction and let it fall back to neutral, it would flip back too far, registering movement in the opposite direction of the axis. Not really a problem for games like Dark Souls, but for platformers like Spelunky and Axiom Verge, it would change the direction of the character--extremely problematic. With the above settings, platformers work fine. I would imagine that this would eliminate the kind of drift you may experience.