The Smooth-On “Epsilon” epoxy coating will not eat into the foam, but does seem to adhere to it well. I have found that it will protect the foam from the gelcoat, even when applied in (or sanded down to) very thin layers. The down side would be the extra time spend applying it, as well as the cost. By the time you factor in the cost of the coating, would it still be less expensive to go that route, or would you be time and money ahead to have either gone with the correct foam or just use the epoxy gelcoat on the Styrofoam?
The “Epsilon” coating is pretty easy to work with, but does tend to flow continuously until it is fully cured. The directions state to ‘keep and use at 73 degrees (F)’ and that is pretty accurate…not 68, not 71.6, but 73. Okay, so it may not be THAT precise, but it takes significantly longer to cure to a sandable hardness with the temperature even a few degrees cooler, at least that has been my experience.
I would suggest either making sure whatever surface you apply it to is fairly level (to minimize flowing), or let the epoxy start to cure and become thicker, then spread it. Even after it starts to become very thick (similar to the consistency of caramel, maybe even a little thicker), you can still spread it nicely with a plastic spreader/squeegee. This way it will cure shortly after you get it where you want it, and your chances of ending up with thin spots will be minimized. This may not matter at all if you do not intend to sand it, but obviously you will want to coat a little thicker than you need if you do want to do some final sanding and shaping. So again, this would add even more time to the process of making your part, but could possibly be worth it to get it the way you want, using the Styrofoam.
Some time in the future, I intend to try machining some fairly simple shapes and patterns into some EPS (I’ve been using the pink insulation foam), making the initial cuts oversize/deeper than necessary. Then I will apply the Epsilon coating thicker than necessary, and run another final machining program to cut the hardened epoxy to the size/shape desired. I don’t know that this will be any easier than machining a mold out of another substance, but certainly will be inexpensive.
Good luck with your project, and I hope this helps!