Well, if you're parking it on grass, just get some Woodland Scenics turf, as fine as you can get, in the railroad section of you LHS. Cover the plaque with white glue, you don't have to make it square, just so it extends beyond the edges of the aircaft and sprinkle the turf on it so the glue is fully covered. Dril a hole in the base where one of the main gear will be and drill a hole at the bottom of the corresponding wheel Place a piece of brass rod in the wheel and super glue the plane to the bse.
Now, this isn't a diorama, since you're not telling a story, just placing an aircraft in the environment.