Confession: I have not built a true foamie - but I have bonded sheets of foam together! Personally, I avoid liquid-applied adhesives because I'm impatient :p so instead I like to use tapes. I have not yet used Great Stuff to bond the foam, so that might be a better solution. But if you like the ease of tapes, Gorilla Glue tape has worked for me, and I'm curious to try a 3M VHB tape.
Then again, if you lap the joints, I don't know if a surface tape would be necessary ... Personally, I don't feel comfortable just gluing any butt joint, foam or otherwise. For that, I've always used Gorilla Glue tape - but that's cause it was easily available, not necessarily because it was the best tape for the job ...
Eager to hear what others have used.