I'm a big fan of polyurethane (Gorilla) glue for foam / wood use. You can heat and it will turn to water just like epoxy, but will begin to cure quickly, so make sure it's close to where you want it. The advantage of the poly glue is that it foams up and forces itself into the foam so you don't get any voids.

If you know any diabetics, you may be able to get ahold of some syringes to put the glue into the voids. Fill up the syringe, then run under hot water to heat up the glue. You could also do this with epoxy. . . .