I'm interested in purchasing BR111 7/16" solid flooring in Santos Mahogany but I have a transition problem. The floor will be meeting two adjoining rooms with marble sills. The height on these sill mesures about 1 1/8", because the foyer has a wet bed. What would be the best way to raise the height? My thought was to put 3/8" plywood, what would be the best way to secure nail and glue? The other way is to find some 3/4" solid but in BR111 it's almost double the cost.