I've tried five times now to tune my 5002v58 to standard tuning (GDAE) and can get the high string to within a half-note of the target, and turn it any more and it breaks. Sometimes at the ball, sometimes a random spot on the string. Five times. I've "solved" the problem by tuning the whole instrument down a note. But this isn't a great solution IMHO.

BTW I've tried a variety of string thicknesses, from .09 to .115. They all have the same result. Get SO CLOSE and then TWANG and there's a string sticking into my arm and me writhing in pain

This is not normal and your choice of gauge is within range, at least on the low end, although the actual spec is .010. I have to think there's some kind of a burr or sharp spot on the bridge, although this doesn't explain a break at the ball. It could be as simply as the string binding in the nut such that as you tune it, tension builds up and then the string slips suddenly, causing the break. To start, you might lube up that slot with some pencil lead or worst case, opening up the slot a bit.