Great intro into the labyrinth of laser cutting Splinter.
Gotta admit I immediately thought laser engraved as opposed to the heroic cutting of veneers... though engraving could leave little stock "under" the engraving.
I've never tried cutting veneer per se on the laser as I was always intimidated on the air blowing small pieces away.
just my 2 bobs worth...
I've always laminated veneers onto 3mm (or dressed down further) MDF and have some meat bacon rasher (size) to cut through.
When I cut inlays, I cut upside down on the assumption that the kerf is a fraction wider at the top and narrower at the bottom where the laser strength is diminished. During assembly the minor bevels will assist in jamming the pieces together. This is probably irrelevant in your scenario, however, it is a method that has worked for me.
If your first cut is too short... Take the second cut from the longer end... LBD