Mike~
I've tried Styrofoam glue (in caulking tubes) and Gorilla Glue and Titebond/Elmers - but I use epoxy from US Composites - got the idea from this site - much cheaper than WEST and I've liked it so far. I think it's at least as inexpensive as gorilla glue ounce for ounce - and I always have some around the shop. Also, I coat the foamer with epoxy and sawdust (haven't tried burlap yet) so I need it for that phase as well.
It IS much harder than the foam and you need to contend with that when shaping. I use a coarse rasp alot on foam and I'm just careful to hit the epoxy line at an angle with the rasp.
Also, I use 1/4" AC ply bottom board - give some to attach (deck screws) the keel to, to protect the "chines", and to give a bearing for the SS screw eye with which I attach the head.
I clamp the sandwich (here 3 pieces of foam plus the plywood bottom board.) with a woodworkers clamp (any deep throated clamp will do) - but you need to fuss a bit to make sure the pieces do not slide around. I use wooden toothpicks to register the pieces.
For a tail insert, I use 1/8 plastic (cut from an industrial drum lid from my farmers) but plywood or masonite will work, esp if sealed in epoxy.
Foam is a great medium for beginning carvers - of any age. And, if I were making a goose rig, it's what I'd surely use.
All the best,
SJS