Oh and there is another variant of Flow where you map things between a base curve and a target curve, rather than surface to surface. But that curve-to-curve based flow will not work for this kind of non-uniform stretching that you want to happen here because the curve-to-curve one matches distance as traveled along the curve.

The surface to surface one matches UV space to UV space, so any deformation of UV space like bunching or spreading of control points will have an impact in the surface to surface one.

- Michael