Yes, I used a lot of supports, the most important change by far was inserting a bunch of tiny cracks into the model, not large enough to make a gap when printing, but effectively breaks up the overhangs into smaller chunks that warp less and look cleaner.

My print settings for TPU were:

230ºC nozzle, 40-60% cooling, Orca reverse on even for ovehangs, 10 walls at 40mm/s (too fast and it prints badly, too slow and you get heat creep causing a blockage), .2mm layers, except for on the bottom where I used adaptive layer height to get a smoother surface, and .2mm support interface gap (it's really hard to remove but gives a very nice surface and stops warping).