Good start by the looks of it - what will melt it and what won't depends a lot on the kind of plastic it is, definitely test on offcuts / scrap first! Bear in mind that resins & epoxy may also release chemicals while curing, so be sure to test it on offcuts with mixed resin first. It's quite possible to have a resin that doesn't appear to dissolve the foam at first, but will gradually eat away a thin layer, so test on a scrap overnight. Of course, if you intend to remove the foam, and the resin sets before eating it you may get away with it
You'll also want to check whether the foam in question does dissolve in the solvent you intend to use - polystyrene melts like nobodies business with acetone, but depending on the plastic YMMV... that stuff looks like you could dig it out after the fact easily enough though.
For reference, epoxy resins generally have mix ratios between 1:1 and 5:1, while polyester resins only use a very small amount of hardener, generally in the range of 20:1 through 100:1. I've used West System epoxy and generic solvent-free "marine" epoxy with good results on styrofoam, but some epoxies do contain solvents that can attack plastics. Marine grade epoxies should generally be OK, as the volatile solvents which attack plastics would also leave the cured epoxy slightly porous, which would make it unsuitable for marine use.