It is really not possible to fully restore mangled (technical term) threads. A cutting tap will simply cut new threads in whatever material is left and that leaves a very weak threaded hole. A forming tap (the 'thread restorers') will re-form the threads to a degree but some material will no doubt be lost again resulting in weak threads.
The better way to go is to have the hole resized and sleeved. You could do this yourself but given the expense of the tools (drill, tap and the actual sleeves) and considering there is a learning curve to use these sleeves, I would suggest finding someone who would do it for you. Larger motorcycle shops often do this as a service. Once a sleeve is in place, it will be stronger than it was originally and as the new threads will be either steel or stainless steel, odds are that you will not have any trouble cross- threading a screw again, at least not in that hole. The service should not be overly expensive. Make sure whoever does it cleans up any chips that end up in the frame though as that is part of the induction system and behind the air filter- any chips introduced in the frame will end up in the engine shortly.
Brian
So checking out my battery the other day, and putting the door back on, I had the bolt crooked I think. Tried to finger tighten it, then realized the err of my ways, backed it out and tried to correct it. No go. I didn't want to do any more damage so I sinched it down at what I think was the correct angle, but I didn't want to force it all the way. Its only what, a half inch of threads in the nut that is welded to the frame. Can I even tap that out again? What to do.