Damn that sucks bro, those long bolts are the worst case scenario as far as broken bolts go, your idea could work if you’re very careful, or you would need to find a skilled machine shop to completely drill it out and tap it. Sorry but if not you’re SOL & need a new case.
I almost had the same issue but luckily the boat didn’t break completely it was literally hanging on by a thread as you can see in the pic. Only tighten these bolts with a Light snug ONLY! Let us know how you make out and good luck.