Looking at that style of Pitbull tune-o-matic bridge I think I would try:

1. sinking the posts deeper, so the lip sits flush with the body.
2. filing the underneath of the bridge where it sits on the posts (or getting a thinner bridge),
3. filing the saddle slots a tad deeper.

Since the strings are a couple of mm high at the 12th fret, you will need to lower the bridge by twice that amount! Still all very scary!