Changing the start and end points of each cut line in LaserCut 5.3 or Corel Draw

I do a lot of designs where there are small gaps in the cut lines. Using Corel Draw 2017 and eCut6, I can take any solid area and make little gaps in the perimeter. If you make a square and put a circle inside but not touching and then make gaps in the circle and laser cut it, what you get is a square with the circle not cut all the way around, but hanging on by little tabs. This is exactly what I want. Mostly I'll have many objects within the square. So, when I pick up each square, all the little shapes come up with it.

The Problem: When it laser cuts, it starts on the left, cuts to the right until it oomes to the end of the line where there is a small gap. Then instead of starting the next cut just across the gap 1/8" away, no, it jumps to the end (to the right) of the next section and cut going left. Very inefficient! I asked the folks at Jamieson Laser how to fix this and they could not figure it out.

The Question: Is there any way to 1) change the start and end points in each line, or 2) is there same software the can take the dxf file and automatically order the cutting in an efficient manner?

I need to solve this problem because sometimes it takes moire than a day to do all the cutting for just one job. That is a lot of cutting! Got to get more efficient.

Juli in Kona