I'm a new guy here, but have about 25 years of composite construction experience in the high-performance marine world. I didn't read everything word for word on all of the responses, but let me attempt to give a little help, if I may?
typically, you cannot directly cover many foams with any form of resin, that contains styrene (polyester and vinylester resins). Styrene is the stuff that makes that smell of "bondo" we all know. If you want to safely cover a foam you are not sure about, brush on some "neat epoxy," that is, unthinned epoxy. When it begins to "tack up," apply another thin coat. This can be done with a brush or roller. Also, use an epoxy that is "non blushing" which means upon hardening, you will not need to remove the "amine blush" from the surface. Amine blush is a natural process that occurs to most epoxies as the hardening takes place, and the air and humidity are hitting the surface. Upon hardening of the epoxy, scratch it lightly to prep it for any paint, or finish you like, or you can fiberglass over the epoxy, though weight is a concern. If I were doing it, I would apply a coat to the foam, allow it to tack-up, then apply another coat, and as it begins to tack-up, I would apply a very light, one or two ounce cloth, if you are just trying to make it more durable. Use s-glass if you can locate it, e-glass is good too, s is better. stay away from carbon as it is stronger, however, when it does fail, it fails disastrously. This is also the problem with vacuum-bagging, though
vb does lighten the finished structure, by removing unneeded resin, and allowing the proper resin/cloth ratio, it also is more likely to damage upon many impacts, as it is not as flexible. When creating any structure, you have to find a balance of strength, weight, rigidity, and cost. Notice that strength and rigidity are not the same thing. Think in terms of a 1/4 inch thick piece of plywood is much stronger than a 2 inch thick piece of extruded polystyrene board, but the extruded polystyrene board feels much stronger, as it is so much thicker. I don't do a lot of forum stuff online, but saw this. if you have any questions about what I stated, please feel free to call me at 443 975 8469. thanks