You should be able to glue the tiles with a "gentle adhesive." Or as you suggest, be sparing with the fix. Apply a dab on each tile and press it in place.
I have an acquaintance who was dissatisfied with the tiles in his rental apartment. He tiled and grouted everything on a 3mm masonite board, which he then attached over the existing tiles. When he moved out, he took the board down again.