What about something like a rag quilt/faux cathedral window? Take the bandana, place it down diagonally. Put a square of batting and a square of fabric (like a solid) on the diagonal bandana so it looks like a square in a square. The square on top would need to smaller than a full square in a square. Stitch two of these together, bandana sides together. Top stitch to hide the seam. Tie the triangle edges of the bandanas together.
This can be tested by making a single square. You can verify that the square is the right size to be able to tie the corners of the bandana together.
I hope this makes sense. I'd have to make a square to photograph it.