Epoxy resin can be used with polystyrene foam which could assist with the structural need. More expensive I believe but this isn’t a huge job. It is easy to work with you just need to isolate yourself physically more from the material (contact and vapor) as its effects are cumulative.
Alternatively, now that you know what you want to do, you could now model it up using urethane foam which works fine with polyester resin.
Additionally regardless of which foam you use, you can glass the show face side and then working from the back, carve out additional material down to the glass layer to create ribs and then glass that side.
Another thing you could consider, Great Stuff is urethane foam. If you were to apply a veneer of Great Stuff, sand it to the surface you want creating a continuous surface of urethane foam you could then glass that face. Then after the one face is cured, you could apply polyester resin to the back polystyrene foam and it would melt to the back of the urethane foam and surface.
If you decide to go the urethane foam route, you should be able to get it cut in 1” slabs. Use the 2lb per cubic foot material, it is strong enough to hold the surfaces you want but light enough and soft enought to work easily. You can use Great Stuff to “glue” the layers together so you don’t add another material that has different properties/strength to the mix. You might be able to buy one of the urethane foam insulation boards at a lumber yard and remove the plastic/aluminum face to get the material you want since you only need a sheet 4’x8’to do this project.
If you go too deep while sanding, you can use one of the Great Stuff versions to add material back on without having to use adhesives or other materials (like spackle/joint compound). Once you get the front glassed you can then go on the back side and remove most of the foam as well as create ribs, embed fasteners and so on to make the entire assembly work for you.
Urethane foam is a thermoset material, when you sand it you are sanding through the rigid edges of bubbles. The dust isn’t good for you (its an irritant, not deadly like asbestos) and gets everywhere so wear a mask and wear a long sleeve shirt. It also gets a static charge as you sand it (something I am sure you are
I assume you are going to sew a skin of leather or vinyl to cover all of this or were you thinking Rhino liner or another material as the finish?
The course mentioned by Eastep:
https://www.eaa.org/en/eaa/aviation.../composite/building-composite-aircraft-part-1