When you say "way to damp" I assume you mean foam, yeah?
It sounds better with the foam though.
I actually want to get some of these and affix them to the screws on the bridge pickup since I never use it anyway
Anyhow you'll fix it will affect the look of this beauty... maybe you try some (self made?) rubber or foam* bridge pieces, depending density 3-5mm should last (just a guess of course) forming them with fine scissors when string mounted.
*Why not trying Styrofoam?

