Was wandering around Home Depot (again) recently. Discovered a new (to me, anyway) double-sided adhesive sheet material intended for installing tiles without messy thin set mortar.
It is also great for "gluing" styrofoam sheet material to each other or to plywood, etc. So far, I have used it to install carved foam cliffs on plywood backdrops for the club's new modular layout.
It would also be great to glue up multiple sheets of Styrofoam for carving landforms. There was always a lot of down time waiting for glue,caulk, or liquid nails to set enough so I could get to carving. With this stuff it's instant grab. You wouldn't have to cover the whole area to be glued - just a few squares of the stuff here and there is all you need.
It would also be great for installing building flats on backdrops (permanently!), or sticking rock castings to cliffs before caulking around them with plaster or Sculptamold, or installing roadways to the table top, etc, etc. It would work anywhere you would normally use a contact cement or where semi-flat materials are to be attached to other flat surfaces. The stuff is powerful enough so you don't need too much contact area for a good grab.
It is very permanent though. I doubt if you could separate the pieces once stuck together. So don't use it to attach building flats if you will ever want to remove them.
You get nine 9"x18" sheets (about 10 sq ft) for about $20.