Great to hear you got it solved, getting my head around the fill function took several weeks work for the same reason you ran into. I have also solved many issues in laboriously long winded ways and later found shortcuts.
As far as the start and stop point on your cut what about including a small overcut on one corner so that the cut starts outside the perimeter and actually cuts over itself at the corner leaving the start and finishes outside the required outline. The arc may not be needed to complete the perimeter if the overlap in cut separates the outline.
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