The solution was obvious.
To the fabric store!
Rather to my surprise, Joann's actually had half a dozen cute flannels in orange and turquoise. So I got them. And prewashed them so they'd shrink before sewing instead of after, because that's just annoying.
Yesterday afternoon I lovingly, meticulously, made three big squares, each with a different pattern on each side and cut out on the grid so they had actual right angles and genuine equal sides. I poked the corners out and ironed them and topstitched all around so they'd stay put. Boy howdy. I did them right. Besides being nicely absorbent, they'll be good to lay her on or to cover her feet when we're out and about, or for a nursing cover in a pinch.
But that sort of precision is exhausting and took like three hours. I took the rest of the flannel, sliced each piece into quarters without measuring, and zigzagged around the edges. Boom. Done.