Welcome back, and Interesting!

You could try lashing the soaked 1/2 squares wedged apart the amount they are out of true when dry, and letting them dry.

Another odd thing I came across not too long ago; The cheapest white vinegar makes balsa VERY limp. I was able to wrap straight grain 1/32 around an X-Acto #1 handle without splitting. When dry, it held shape.

Two considerations: I have no idea how this affects the strength of the wood afterward. And, thin sheet can be saturated thoroughly, but will 1/2 square soak that deep?

Besta luk!