Epoxy is the best option. A boat grade. Like WEST, RAKA, System3, MAS. The stuff is actually a lot cheaper than it was when I got into boat building around 1980. Will not melt foam. And it has the perfect consistency for lamination as it comes from the bottle.
Here is famous yacht designer Kurt Hughes, talking about the material he used in his tiny house, which is made of pink foam vac bagged to plywood, in the form of a lunar lander. He used fairly heavy ply, but I have used even 1/8" doorskins and the end result is massively strong.
https://youtu.be/PCoymiQ13s8?t=235Using a really thick material like pink foam you are not going to get all that much strength in rugged abusive situations, like boat building. He would use a structural foam in a boat hull. However, in materials where defining a space, stiffness, and in this case, insulation are at a premium, it is good enough.
I think someone asked what the increase in strength would be with 3 layers vs 1. Strength is squared. So 3 squared in 9, and 1 squared, is one. So your strength increases 9 fold. Stiffness is a third order thing, the cube of 3 vs the cube of 1, so 27-1. From an engineering by the seat of the pants perspective, you can get deceived by materials of this type, as the stiffness rises faster than the strength, from the math. But with a foam one can really pile on the thickness. If it is overloaded (not too likely in the case of a teardrop shell, it will fail catastrophically. It seems fantastic because it is unreal in stiffness. Foam is an incredible material, but blue/pink foam is relatively weak. Stuff is so cheap in the US, it might be worth considering what some cheap structural foam like Carbon Foam might cost.