I looked ahead and saw puzzle four's digit set and hoped that it would include all symmetries of a square. It turns out to only have one reflection.
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You're right it doesn't take full advantage of the F shape. I just needed a set of four symbols (in this case it's the four rotations of 'F'), each of which transform into a new symbol when reflected over the northeast diagonal. I do hope to make more puzzles with that symbol set in the future. Edit: In the second version there will be multiple options to pick from.