Here are the results of some testing. Some success but not quite good enough for your obj model.
Your obj, yes unwrapped strangely. I was able to get it to a rectangle in a few seconds using the edging tools but it did not remove the bad stretching that was in the first unwrapping. Edge tool location (Mark seams tab / select edges / edge tools appear left side of lower menu bar.)
Method I used. Select an edge, select edger, select edge loop and then select Horizontal or vertical depending upon my edge selections.
I had much better luck on a similar curve I created in Hexagon plus a really bendy one I also created. I used the same method as above after unwrapping.
I could use the brush tool to relax a few areas on the final rectangles without meshing up the outside straight edges. I did not do it in this case.
I would send your obj file to Andrew to see if he can figure out what is causing your obj to go bonkers in the unwrapping process. If it effects you, it effects others as well. Maybe it's how 3DCoat reads obj files created from different modeling programs, just a quess though. I also found a few small problems as well, possible bugs in the unwrapping area of 3DCoat.
The first two pictures are the final result of my curve models.
The second two pictures are the first unwrapping.
Your final rectangles are the last picture.
I can see areas in the unwrapping process that would be helpful to have as your suggestions have stated and I like to test to help solve problems plus find bugs. I hope this helps in some small way on your problem.
* a note. your uv island needs to be place horizontal across the uv space for the horizontal and vertical tool to work correctly or it seems that way...
If your want a free copy of the full version of Hexagon, Daz3D is giving it out till the end of April for free. Everyone has their modeler and Hexagon is mine for a number of years. Maybe you would want just to use to for testing purposes...