I am looking at using Polystyrene foam insulation sold at Home depot to use as structural supports that will be epoxy fiberglassed over. I am not sure if the resin will adhere or will it melt? Has anyone else done this?
My plan is to use it to support my front deck on my 12' jon, the deck itself will be plywood core. I just need it to make a framework and the fiberglass will be the actual support. Since it will be glassed to the bottom of the boat, I do not want any wood that can rot if water finds a way in. I plan on putting flotation foam in between the ribbing before the deck is screwed down.
That idea will work as the foam will be covered with epoxy and glass much like a stringer. Since your boat is fiberglass screws are not the best choice. Just use thickend epoxy to use as glue. If you do not want any wood then you could use one of the fancy foam products that are available such as the ones Karl mentioned as well as others. These are expensive but will never rot. You are in the area of Michigan Composits - they make a nice product that you might be able to get cheap if you go there and see if they have some sheets they screwed up - could also use these for the supports you mentioned.
I've done some experimenting with R-max foam, and normal polystyrene/styrofoam covered in multiple layers of epoxy and glass. After several different layups and strength tests I will tell you it will NOT be part of my boat! Remember that not only does it have no compressive strength, it has no structural rigidity so any twisting force, which is always present on a small boat, can buckle it.
I also found that by the time I had enough glass to make it fairly stiff, it weighed nearly as much as the plywood would have. It's not worth the risk, or the expense. Just stick with some plywood and you will be much better off IMHO.