It's been a while since I worked in a shop so I hope my information isn't too out of date. Use the 13 mm screws, they need to be shorter since the mounting hardware is not recessed into the boards top sheet. I would suspect your discs here, unless you base plates are warped. What I would try is simple, and cost you a lot less than new bindings. New discs and hardware first. You should be able to get everything you need with two phone calls, one to C3 and the other to Burton. I wouldn't be surprised for free. Try replacing all your hardware M6 sliders and bolts as well (due to heavy tightening something could be bent slightly) and the discs, before dumping two or three bills on new bindings. What do you have to lose by trying that, 10 bucks or so?
Don't cut off the head to stop the headache first. Try the cheap route, if it still is screwed up then I would replace your bindings because your baseplates might be warped causing play when the board flexes. Hope it's just the discs, good luck.