I would use nothing but the DAP glue. I have used the counter top adhesive in the past but found something I like better (DAP Vinyl top adhesive)
Tried them all and in the Illinois heat & humidity the 3M stuff gave up quick...I'll never use it again, caused to many redos.
CAUTION/hint: thin the DAP glue a bit and spray it on with a cheapo spray gun. This will cause the glue to go on dry enough that it won't have any chance to harm the foam (if it would anyway, I never had a problem).
Spray your material and the board and on the material and let it dry to touch, smooth the material on. Just like counter tops...
To prep the board, put some 80 grit on a DA and lightly/quickly go over the board, it takes about 60 seconds to get all the old loose dry foam off. No need to remove the old adhesive, it'll stay there.