How about a feedback mechanism based on the current flowing itself? Have some piezo thing stretch the material with feedback from a current sensor going though that material to have it always go for the highest current flow.
I assume feedback control is an obvious enough approach that the researchers already checked and rejected it - but I'm curious as to why specifically it would not work. In my layman non-physicist non-material-scientist imagination, I'm thinking of an aggregation of such self-regulating piezo "cells", or even continuous surface tuned to locally stretch/contract "just right" with the current flowing over it (is such a feat even possible)?
I think the “tension axis” is more likely to be fruitful in a different way, where we find some structure e.g. a crystalline formation that happens to hold atoms apart with just the right amount of tension. But this is all very speculative - the “tension axis” is just a random thought I had while reading the article!