Sorry, my brain had switched off for the day and didn't think of doing that https://we.tl/t-9giKKi0aRS
Thanks for the file. At first, I wasn't able to reproduce your issue, but then I was able to find just the right amount of mesh distortion that would create this artifact.
We basically get a feedback loop when using LimbIK when you *don't* have independent legs. The best workaround I found was to set LimbIK to "Arms Only" since it works fine with the independent arms, then use fixed pins to stick the feet to the ground instead of LimbIK.
Alternatively, you can make the legs independent, though I really liked how the character moved with the fixed pins.
Really cute character! Nice work.