I do not know if this solution has been demonstrated before, but it has solved my and another user’s problem. I think the difference is that there is no switching of the coordinate system start point. Absolute positioning all the way, maybe even with rotary operation.
I was using my rollers as a bottle support, but not rotating it. I needed a way to easily / quickly synchronize the laser position with the position of the drawing. This series of steps is my solution.
Home machine if capable.
Move to front-left, power up, and Set Origin if no homing switches.
Never move by hand after power on.
 Jog laser to CENTER of what you want to burn.
 In Laser window, click “+Show Last Position” button.
 In Workspace window, you should see a small red cross.
 In Workspace (drawing) window, highlight (CTRL-A) your work.
 Mouse to the center of your work, click and drag that center onto the top of the red cross.
 You now have the physical locations of the laser and work aligned.
 Frame should be pretty close to correct. If not, re-scale the drawing or move your part to be burned slightly, but do not move the laser or the drawing center.
I found this method also allows to quickly relocate to unburned / uncut areas of the workpiece.