I know it would be a significant game balance change, but I think maybe you should be able to flip the pieces.
To me, this was the least fun part. Since there’s no penalty for entering squares incorrectly, I just tried the shape, and if it wasn’t accepted, I figured “oops, I must have flipped it.”
But I agree it would be a major change. If you ever share the source code, I would want to try doing this myself for my own use, to see what it feels like.