Since I've been playing with foam again I took the opportunity to conduct some tests on thicker sections of foam.
The 12mm foam cut in a single pass, 25m/s and 30% power so super fast. The trouble is that the middle of the material gets really hot and starts to melt, drawing back from the beam, this causes the curve you can see on the edge of the cut. The 30mm foam was cut in multiple passes, 25mm/s and 15% power. As you can see the laser caused ripples down the edge of the material for each pass. Both of these are pretty much unacceptable for the majority of things.
The second problem is caused by the way the laser works. As the beam passes through the final lens it takes on an hour glass shape. The neck of this hourglass should be focused onto the surface of the material. As the beam passes through the material it gets wider again at the bottom of the cut the beam is noticeably wider than the top.
These two issues can actually be used to counteract each other. If you aim the focal depth at the middle of the material the narrowest point of the cut is the point where the material shrinks away the most. It doesn't work for much thickness but it does help up to about 10mm thick.