Good suggestion.
Yes, Polyester resin (i.e. bondo brand) will melt styrofoam.
I got epoxy resin because there is no chance of it eating foam - (no solvents).
Earlier I'd gotten polyester resin and set up tests - it ate through every primer I tried, including a coat of spray-paint over a thick coat of Killz. The solvents in the spray paint weren't enough to penetrate through the Killz, but the polyester resin seeped through over the few hours it sets and slightly deformed the surface into a pock-marked bacon.
The only thing I could find to work perfectly was to coat the foam in a layer of aluminum tape, then resin over that.
But I hadn't tried (or found) a styrofoam specific primer.
In any case, I went with epoxy to eliminate the problem altogether -
However, it looks like I might be very allergic to the epoxy.
I laid up that sample yesterday with nitrile gloves on, being very careful not to get any on my skin. Within an hour of finishing I was weirdly itchy and sunburnt/rashy feeling in various phantom places all over my body, but mostly face and neck (the only skin exposed when I did the work). I still feel a little weird and itchy today.
Since the epoxy works so nice with the foam (and it was so darn expensive), I'm tempted to try another session with a Tyvek suit, respirator, swimming goggles and barrier cream (all these suggestions I found online). Still, I'm a bit spooked, because apparently expoxy resin allergy gets worse with each exposure.
I saw on an RC plane message board that they use water based polyurethane varnish to seal EPS. I already have some of that, so I might try a tester piece.
Does anyone have any other suggestions?