"""""""""Is it possible to add an option where the new line (curve) could be made with control points matching the original curve, but straightened out?""""""""""

So with this in mind, I copied and pasted the original points, then used BoundingBox and centered the points on the new "unwrapped" line. Used the scaling widget to flatten them down to the line.

I suppose the question though, would be:

"I used scale from center", to bring the point stucture into length with the new line... Does that distribute them "Properly"? or is it just close. Would a "stretch" be different? Like distorting it more?