Hot Wire Foam Factory has a product called Foam Fusion that sets quickly and bonds permanently. It looks like Elmer's glue but is not. It creates a permanent bond, it's inexpensive at about $7 for a large bottle and you can cut through it with foam tools. It also has a long shelf life. I bought a bottle of it 2 years ago at Trainfest and I just used it a few weeks ago again. I like it a lot.
I've used carpenter's glue in the past and that works good, too, but it is harder to cut with foam burning tools and harder to sand, too.
Mike