How to plug up stop tailpiece holes on a les paul guitar?

Looking to install a Bigsby B-7 vibrato on a Les Paul Style guitar, but one of the holes for the existing stop tailpiece is exactly where one of the Bigsby screws is supposed to go. What would be the best way to plug up the holes left by the stop tailpiece so that the Bigsby can be attached properly?

Better off getting a vibrato that's a better fit. Sorry, but the only solution to properly secure it is to add a block of wood inside... and that's not going to be easy or good for the guitar.