the tremol-no works decently well to lock down the bridge but doesnt provide the added thickness in tone/sustain increase of a fixed bridge conversion..
filling the cavity is a big job..might also have to involve a refinish, definately major $.
what i've done before is to get a block of basswood/hardwood of your choice, cut and sand it to fit in the rear cavity and block off the trem making sure to get a real snug fit, and as much contact as possible. works well, and removable too.