tile countertop edge question
We recently had an island surfaced with porcelain tile. Between the tile and the cabinet top is 3/4" plywood, then about 3/4" thick mortar bed, and of course a little thin set. The installer put a 2" thick strip of tile, vertically, around the edge, on the underside of the tile countertop. The obvious problem is that there now isn't room for the top cabinet drawers. The installer insists nothing can be done except to cut down all of the top drawers around the island by about 1/2".
I'm not trying to rag on the installer. I'm wondering if anyone has run into this before and, especially, I'm hoping some of you might have creative solutions for the problem.
He used a perforated metal strip along the vertical edge of the countertop, and I'm worried it might be screwed into the face of the cabinet frame, where the drawers should be. And then there is backer board over the metal and then the tile edging.