You could restring the guitar and wrap the strings as if the tuners were standard tuners, if this works and the guitar stays in tune then I would say its locking mechanics on the tuners are bad.
overtightening the locking on tuners can ruin the mechanics that lock the strings, I don't belive this can be fixed, but a new set of gotoh magnum locking tuners would be around $70.
I would make shure its not catching at the nut first.
You can't overtighten Gotoh's, they lock themselves as you wind the string, there is not a thumbwheel like you'd find on other types.. I'm thinking its a nut issue.