Combining TriAx with General weights?

Faux2D

I'm wondering if there is a way to use TriAx weights for certain bones and General Weights for others. Triax is great for skin-tight assets but it seriously messes up when dealing with translation. I tried the "Blended TriAx/General" option but it didn't do anything. I also tried deleting all the XYZ TriAx maps and leave only the General one but nothing happens. The bone is moved, the selection is filled in with red, but the geometry is not modified at all.