UV re-mapping

Hello there I am hoping someone can help solve the following.This is a follow up to a previous post, I thought of a different angle…
I have a bunch of rolled pipes (planar, single radius) which are arranged to create a double curvature surface. All center lines meet and intersections between members have been resolved and modeled.
From a fabrication standpoint, the process we would like to follow is to laser cut/mark the scallops at the ends of straight CHS before feeding them to the rolling machine. In essence the fabrication process is the reverse of the modeling process.
I am trying to translate these single radius planar pipes with scalloped ends into straight pipes whose center line is the same length and where the scallops maintain the correct position.
The solution could be to remap the UVs of the pipe to a rectangular arrangement, such as in one the attached pictures, approximating a reversal of the compression and tension that occur on the inner and outer faces of the rolled pipe.
One of the issues I am encountering with this approach is that the UVs of the piped arcs are on what appears to be an arbitrary plane rather than having a relation to the plane of the arch they are piped from.
Also any help towards a definition to effectively remap the UVs would be magnificent.