send it to me, i'll fix it.
on a more serious note, what you're hearing is 3rd bridge sympathetic harmonics. raise the bridge really high, shim the neck to compensate, and see how it works. that should diminish the harmonics, but no guarantee. the only way to get rid of all harmonics on any 3rd bridge is to mute it. you could do this with strips from an old t-shirt or something.... however,try less-invasive methods first. 3rd bridge harmonics actually sound really nice in my opinion, but if theyre really loud, maybe not...
oh yea: are the sounds you hear from the 3rd bridge sympathetic, meaning that they are harmonics produced by the notes you play? ie do you get the same notes that you're playing? try raking and seeing if you get sound behind the bridge. if you do, it would mean that the picking action is making the 3rd bridge sound, not the notes you're playing. that probably wouldn't sound too good.
either way, start with raising the bridge and shimming to compensate.