Papa, I have a 30W CO2 laser (according to Splinter... I'm no techo)... so no, I don't do anything to reduce burning other than the first setting I ever tried.
If I have to cut >6mm then I do have issues and that's why I try to work in multiples of 3mm and 6mm MDF (or solids) as their thickness is within Chinese tolerances. While I like solids, MDF is a tad more predictable and for my use, MDF is good enough... and when polished with the Beall buffing system, it's tolerable by most others.
The laser seals the MDF 'endgrain' glue content to assist glue ups and assembly... depends on ones outlook fortunately/unfortunately, I'm not the greatest experimenter and when something works for me, like shite to fur, I'll stick to it.
If your first cut is too short... Take the second cut from the longer end... LBD