Everyone who owns a jaguar or jazzmaster goes thru this crap. its the absolutely worst designed bridge in history of bridge design!
Buy a Gotoh Nashville tune-O-matic bridge and use that, you wont have any more problems after that.
You cant use the mustang bridge because the blacktop radius is 9.5 and the mustang bridge is 7.25 but with a nashville bridge you need to file some slots in the saddles anyways so you can correct the radius from 12 to roughly 7.25.
You will likely need instructions installing it but its very simple. All you need is the bridge itself, a small set of needle files and some electrical tape/or aluminum foil.
There is no permanent modifications done to anything other than the bridge itself,none to the guitar whatsoever.
If you buy the bridgelinked at the bottom of this post, PM me and I'll help you install it.
first bridge on the page
Needles files like these ones:
