I would think, butting the shim, and having a good strapping to keep it together despite the cut in the shim would make you able to put the the rivets/brads in the shims on either side of the cut. If you do this, I'd personally think it would be a good idea to maybe try to level out (maybe with some putty?) the hight difference that occurs when the shim is put in from the back, to make the shim more invisible from the outside.