RE: Super Glue // Epoxy Glue
Just like glues, there is a vast number of foams out there all fitting under "common" names. Stating with conviction that so and so is wrong is the height of stupidity and flat out ignorance. Whoever puts forth these absolutes, is completely clueless. They are probably generally right about common materials one can find at your Ace Hardware store, but otherwise they are smelling some serious sulphur gas particles because their heads are up their *****'s.
Most glues, while maybe not ideal, will stick well enough to do the job. His elmers glue for instance It will depend which version. Standard elmers works. Waterproof elmers I believe melts styrofoam. IE tightbond II I think. I could be wrong. It could be tightbond III. I have used it on foam. It works. % years later if you pull the panel off the foam one will still have non dried elmers glue but it will stick especially if its wood allowing the water to evaporate through the wood. You said fiberglass over the top with CA wicking. That will work. It will be brittle of you use the super fast CA one can normally buy. Just like any glue, CA is a GIGANTIC family of glues. The slower it cures, rule of thumb(not always true like everything else in life), the less brittle it will be. Covers everything from ultrasonic curing CA's, to UV curing CA's, to water curing CA's or a combination of many factors.
Depending on the foam type(polyurethane, foamed PVC, foamed ABS, acetate, etc), you could do the repair in rubber cement if it is not styrofoam, not ideal but super cheap and easily brushed on. Spray/brush on, let it get tacky then apply fiberglass and brush or apply glue of choice. Make it thin.
Heck, I have used wall plaster mud to "glue" foam together when I wanted a 6" block. It is amazingly good actually when spread VERY thinnly and allowed to predry a bit. It gets wet you have a problem of course along with high vibration environment.
I personally have taken to skim coating my styrofoam with a 2 part polyurethane foam/glue, take the ridges/bumps off and sand then apply whatever I choose as long as it is well ventilated. Can make a foam airplane in a whopping 1 hour this way that is night indestructible depending on what one uses for a surface if one uses anything at all. Assuming one doesn't just use colored tape of course.
When it comes to foams/glues its trial and error.
Emphasis on error generally.