Congrats, you've rediscovered low tech honeycomb composite panel making...

The idea of two strong skins with a separator between is a very strong method that can be made quite light. It's not new but it's often forggoten.

Another option instead of wood for the side skins is to lay up fiberglass and epoxy resin on two glass plates that have been well waxed with mold release wax. You'll want to use a layup of tapered glass so you get the strength where you want it and light where you don't Then lay the foam on one and set the other on top layup down. Set some weights on it and then let it cure. After it cures you pop off the glass side molds for a super shiny and smooth profile. The wood hard point inserts is also a great idea.