Boys (and Girls) with the lasers... what input does it take to run/print...

I use SketchUp to design... of course that is 3D. but I 2D it to generate cut lines that are then printed to a vector PDF.  That is imported into CorelDraw where I tidy it up (if needed) and design the vectors for engraving. 

From there I can then just print to my laser like any inkject printer and the cut/engrave is governed by the color and thickness of lines.
Coloured hairline lines are cut in a set colour sequence, and anything black is engraved.  CorelDraw can export to many formats.

If any of the formats can be used on your machine, you just need to ask (no need for home delivery of pellets of cask-o-vino).
These are the exportable formats from CorelDraw,
   

From SketchUp,

If your first cut is too short... Take the second cut from the longer end... LBD