What if you fused lightweight non-woven interfacing to the back of the panels? Obviously it would make them thicker and heavier, but it should help eliminate the twisting you might get if you sewed those wonky squares to your other fabrics. Hopefully, the printed pictures would remain square. I've done this will small pieces of printed plaid that I wanted to be "square" despite the off-square print. I love the colors in your panels!