Looking through some .au websites, I came across Selleys Shoe glue. Obviously, being on the complete otherside of the planet, I can not verify that the product is similar, but it is where I would start testing.
I think part of the magic of the Goop is that it does 2 things (not a chemical engineer, so keep that in mind)
#1 I think the toulene partially breaks down the epp foam, but not enough to cause any real harm.
#2 it fills the voids in the foam and bonds onto the partially broken down foam.