CorelDRAW Graphics Suite X4 :: Duplicate Overlapping Lines On Puzzles?

I know this question was posted back in 2010, but thought I would bring it back to the surface to see if anything new has developed.

I am running X4.  I draw jig saw puzzles in CorelDRAW (several shapes that I andomly node-connect) and each piece overlaps adjoining pieces on all four sides and are connected at multiple corner nodes as well as arc nodes. When sending to the laser for cutting, each side of each piece gets cut twice due to the overlapping lines. I was hoping the RemoveUnderlyingDups and NodeClean macro from a 2010 post would take these overlapping lines and create individual horizontal and vertical line segments from the connected nodes so the laser would make one continuous cut rather than duplicating all the cuts.

However, after running the macros, even on a small portion of the puzzle, I didn't get any results. I combined then broke apart as mentioned and still no joy. The only way I have been able to create separate line segments is to cut apart at the nodes and delete individual line segments... on 1250 pieces, with four sides and all sides overlapping, that's 10,000 separate edits... needless to say, duplicate cutting by the laser is faster.

Ideally, being able to create continuous horizontal and vertical lines based on corner node connections, would be the best. At that point, I could cut a 1250 piece puzzle with just 50 continuous horizontal lines and 100 vertical lines.