I have two methods of transferring the UVs, one that moves the variation's geometry to that of the base geometry before UV transfer before switching it back, and one that does not.
The former (let's call that Former) I get some obvious UV stretching due to the variation's geometry being to different than the base's geometry.
The latter (let's call that Latter) does not have this stretching but has a noticeably different profile for the UV shells which also doesn't look good when the texture is applied.
My solution is to see if I can use both, using the Former's UVs but softly transitioning ti the Latter's UVs close to the UV shell's edges. This would ideally let me have the UV shell profile on the Former while also keeping the distortion fixes of Latter in the middle of the UV shell.
To do this, I would need a vertex or point attribute that has that position's distance from the shell's border in UV space. That way I can transition between the two UVs. Is that something that is possible to do, or is it crazy talk?
Any other ideas are welcome. I included some screenshots along with a hip file.