I would make it thicker at the same time. Guess I forgot to mention that. It should fly better having an actual airfoil.

The way it works is that the thicker it is the stronger it is. If you make an airfoiled stab 3/8" to 1/2" thick the plane will probably fly better and the stab will be stronger. The only reason we use flat slabs is for convenience - not for better flying qualities.

I would use a 1/8" x 1/4" hardwood spar centered in the ribs or perhaps a 1/16" x 1/4" spar top and bottom as a conventional wing. Then sheet it with 1/16" balsa. Make the leading and trailing edges 3/8" wide by whatever height is necessary. You would be hard pressed to fold it.

Then again, I have to admit I'm amazed you managed to fold a 1/4" balsa slab. I don't know much about canards, but considering the small span there either had to be some kind of stress crack already or it was under a lot of G's.