A while back I was working on this problem a bit, then I put it away. I think the cylinder idea is a good one, so this is an example that creates a bounding cylinder on vertical surfaces. It does join all connected surfaces. Joining surfaces into breps does unify the normal direction of each surface, however, it does not unify the UV direction. The UV’s can still be miss-matched, which can be frustrating. This should work for the pictured example.
So, this isn’t a totally universal application. Another way that this could be dealt with is separating each surface by its direction to an input vector, and then a plane could be provided for each direction (perhaps with a bounding box).
UnifyUV.gh (47.5 KB)