I get your point and I agree, I don't think it's a simple transformation. At least not without knowing the different shortcuts.
PMA did a lot of good work with the triangles, maybe we should start looking into a few examples where we have the proper u1 and u2 for a triangle (assuming we KNOW we have the correct values?) and try and work our way backwards from them using the jumping right/left with -f and e. Try and see how this triangulation might work if we have the answers and do it backwards (something he also has mentioned before).
VQC has hinted many times that we should look at larger c's than the ones we have, I don't think it's because the algorithm won't work, but he said the patterns are more visible the larger the c. I don't know how large, though.