My hardware store didn't have the contact cement Maki2 recommended (although I spotted it later at Walmart), so I used 3M 77 and some left over "general purpose" spray adhesive. I ended up getting double sided DuckTape in an effort to save a few brain cells. Using strips on the edges seems to do the trick for securing layers of convoluted foam together and to the base foam enough to prevent shifting. The tape is only 1.41" wide x 8 yards, and runs a little over $5 (ouch). I'm not sure how good it would be for other things.
I'm taking the cover off a King size comforter that has been in service so long the batting is wafer thin. The fabric is still in good and should be ample to make a cover. I have a roll of upholstery zipper tucked away, too. Really, I want to "cheat" and make a mock-boxed cover with the zip on just one long side. However, the thought of wrestling that foam is giving me pause. The alternative is to make an actual side wall and sew the zipper in on three sides, so the top opens like a packing cube. Decisions...