I've seen Doug do the same procedure on Jimmy's Pennsy. He would cut away the old scenery after marking the outline of the diorama and drop it in place.
There's a section on the Pennsy video (available on the link above) that shows Doug doing this. My plan was to use pink styrofoam as a base and build the dioramas on it an insert them similar to what Dave F says. However, I'm building some on Gatorfoam instead of the pink stuff, but I think it'll work just the same, they'll just need to be shimmed to fit.