This is an experiment of wood based composites. This is inspired by Morgan sports cars, which have a chassis that is still largely made of ash wood. I think a piece of plywood, laminated on each side with fiberglass could have a bit more flex than carbon fiber, while still being quite springy, more so than aluminum, but not as violently as carbon fiber due to wood dampening the entire structure.
So I gave it a shot.
I bough a piece of 1/8" birch plywood and cut out a chassis shape:

And I put a layer of fiberglass in each side. I sandwiched it all in plastic wrap and two pieces of rigid wood and the entire thing is under a very heavy slab of granite.

I'll post back in a few hours once it cures.