you could fiberglass it then bondo.
There's a stupid material I used a lot in college: Fiber Hair. It's basically Bondo with chopped fiberglass in it. I think I got it from NAPA, but most decent car repair places should have something similar.
I would make a prototype, make a plaster mold, seal it, then I think I usually used Vaseline for a mold release (
bad idea!), although I eventually switched to KY Jelly (no joke, it worked pretty well), then mix up some Fiber Hair and slop it into the mold. Wound up with lots of airbubbles, but I had lots of filler and sand paper. The vaseline usually would get mixed in with the resin and never really set, so it would need to be sanded off. And the whole finished product was heavier than it needed to be, because it was a lot thicker than a few layers of regular fiberlass and resin. But it generally worked, sort of.
But it might be another way of reinforcing the cardboard, and you wouldn't have to worry about air bubbles.
As another reference, you could try scaling up the old Battle Droid model, or even the old 12" figure, since I think they're both meant to be 1/6 scale. Also good for checking details, maybe.