the
Hipshot Tremsetter will require drilling in the
tremolo cavity to install. While it would stiffen the tremolo, i don't believe it will fix the issues you have raised, especially the breaking the high-E part of it. I have not read of anyone installing one in a UV, maybe someone can post if they have.
It sounds like you need to block the bridge totally or block the bridge from floating. Probably not the perfect solution, but along with the floating trem comes these obstacles. Good luck... glen