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I bought two rolls of TPU filament recently, but have not yet had a chance to test them out (even single material). I'll grab them and run a couple of tests to replicate the behavior you are describing. Hopefully I will be able to find a way to improve the solution for flexible filaments.
In the interim, I do have one thought.......Have you tried upgrading your bearings?
I've seen similar symptoms with PLA when using really cheap recycled bearings of unknown origin in the past. It seemed like the rewinder was struggling to overcome the inertia of the spool and begin the rewind. Adding weight would seem to help some, but felt like a poor fix.
Once I went to higher quality bearings, I never saw this again.
Take a look at the second video on the main page. It shows that the weight of the track alone (no counterweight attached) can overcome the inertia of the cap/shaft/net assembly and generate a full rewind without the filament spool.
Do your rewinders perform similarly, or does the track remain in place when you release it?
BTW, these are the bearings I use: https://www.amazon.com/gp/product/B0094J6GQ0/
The set is expensive ($25), but contains 16 bearings which is enough for a full set of 5 rewinders (with one spare bearing). You might consider giving them (or a similar skate grade bearing) a try.