tl;dr - 2 mm/s retraction speed, 12 mm wipe distance for soft TPU
After wasting many rolls of filament, I finally solved my stringing issue with soft TPUs…retraction rate!
The retraction rate must be very low (2 mm/s here) to make a difference. I was changing all of the retraction settings and following others’ advice, but still my strings were horrible all up and down the retraction tower as on the left of the attached image. Nothing I did made any difference.
Then, as I was cursing the machine for jamming again as I tried to push the extrusion speed up, it hit me. If I push the rate too fast, then the extruder gears deform the soft TPU too much and it ends up stuck. The extrusion rate that works without jamming is low, like 4 mm^3/s. But the default retraction rates are comparatively huge like 30 mm/s. With 1.75mm diameter filament, this comes out to a ridiculous volumetric rate like 72 mm^3/s. There was no way the filament could move that fast inside the extruder. To mach the maximum extrusion rate I was getting, I would need to dial the retraction rate down to just 2 mm/s!
I tried this, and I still had lots of stringing 
But I noticed something watching the tower build. With the retraction rate this slow, the nozzle would actually stop for a second or two during the retraction, and a little blob would have time to ooze out of the nozzle, then it would do its 1 mm wipe and continue. Inspecting the g-code, I could see that a 1 mm wipe after retraction was only enough to absorb 5 to 10% of the retraction, so the nozzle would have to stop for a long time in place.
So I increased the wipe distance to 12 mm. For the first time, I could actually see a few spots on the retraction tower without strings. OMG, FINALLY!
I’m always looking for better ways to print it.