I finally found some time to test this, and sadly it has even more pronounced issues than the other add-on. As mentioned in the other thread it’s a Cycles issue, and isn’t apparent in EEVEE.
It appears to work fine with the displacement modifier, but really needs to be in the node editor to be properly useful. I haven’t checked whether it has frame updating problems like the other one yet.
have you tried turning the intensity down?
Yep. It works properly in EEVEE, so clearly it’s a Cycles thing.
I’m just now seeing everything you’ve been working on, from The Passenger, to the photorealistic Ed head, to your conversion over to Blender! New fan but BIG fan. Thank you so much for continuing to problem solve and get these tension maps working in Blender. Along with your Human rig and upcoming face rig, they are what most excite me about what you’re doing, because I’m leaping into the field of animation for the first time! So thank you!!
hey Chris! love your work; your right click select post is what inspired me to do my attempt at the add-on!
i’m curious about the setup that is causing you trouble. in your example, i’m guessing you are using cycles material node displacement on a subdivided mesh.
with regards to this cycles banding issue, one thing i noticed in my own tests is it seems to be the specific operation of running the tension vertex color through nodes that amplify its strength that introduces the problem (and in fact happens when manipulating any vertex colors with nodes in this way). however, i’ve found bumping up the tension strength directly in the mesh properties seems to give a more expected smooth result.
my guess is vertex colors get interpreted with at a set precision when cycles runs its node calculations on them (although its weird that eevee seems to maintain a higher precision). either way, by doing the strength multiplication when initially calculating the vertex colours, it seems to bypass the problem.
eager to hear if that in fact helps address your issue at all!
edit, just as a visual comparison, i’m attaching 2 cycles screengrabs; 1 where the tension is amplified via the strength value in the tension map properties, and the other where its amplified through node multiplication by a greater than 1 value (causing the stair stepping)
Thanks @JSWilson - happy trails. 
Hey @shteeve, thanks for the work on your add-on! Lowering the Multiply strength and upping the Tension Map strength in the Object Data Properties does indeed improve the situation, however there are still creases that follow the base topology much like the examples in my initial posts.
The displacement modifier gives better displacement results though (plus it allows real-time viewport feedback), so at least I have something to work with for the time being.
