After messing around with this for more time than I probably should have, I'm starting to think that what I want isn't actually possibly, though Jacob's suggestion with envelope distortion definitely came closest. Unfortunately, I can't quite get the image to distort the way I need it to. But thanks for your suggestions, everyone! Who knew that graphing a nonsymmetrical pattern in a circular image to a hexagon so I could knit it circularly (instead of hexagonally) could be so complicated?
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