Fortunately I have the luxury of being able to laser cut 6mm MDF which is flat and stiff enough for my hacking. The "lip" is just a hair short of 6mm and if I measure the thickness of the MDF stock (which varies between 5.8mm-6.2mm, due to cheape calipers used by Chinese MDF manufacturers) and dress it down to the right thickness on my drum sander before hitting the laser beam.
If your first cut is too short... Take the second cut from the longer end... LBD