I wrote something about cutting with a diode laser here. Worth reviewing:
I would say a few strategies for you in this case:
- focus - You really need to make your focus is excellent. You may want to try focusing mid-way into the material in this case
- speed - you may need to slow down to cut to depth
- passes - not sure how many passes you had but another pass may have gotten you through
- air assist - if you weren’t using it this can make a huge difference for cutting operations
- lens - not sure what kind of lens you’re using but a longer focus lens may make cutting easier. Also, make sure your lens hasn’t gotten dirty from trying to cut. MDF is a nasty material and will leave a lot of residue everywhere.