I think I got it. The yellow group at first appears to do the trick but those are “dirty polylines” that double back on themselves with overlapping segments. The orange group fixes them by using Discontinuity to get visually accurate end points and recreating each line.
Curve End Points were useless for this task because they were usually somewhere in the middle of the dirty polylines. I tried various ways to find the pair most distant from each other and stumbled on Discontinuity for that job. Not quite sure why it works…? 
div_rectangle_2020Sep14a.gh (33.4 KB)