I have tried the focus setting on the top and 1/2 way through the material when cutting and it works so much better if you focus on the top of the material with a low power laser. With the 30 watt laser I have I suppose it gives it a bit of a head start getting all the power at the start of the cut at the focal length and the strongest possible beam.
If the laser is focused near the middle then the laser is starting with a bit less power on the very top of the material.
This may work good with multi kilowatt lasers but it seems to be better focusing on top with the low power ones. Kerf width and side taper really doesn't matter unless you need a good join for gluing in which case focus in the middle and reduce speed.
Hey MacGyver! I might PM you soon and ask you a few questions about YAG lasers and the power supplies and what is needed to get one up and running. Seems as though they work really well on granite and marble more so than the Co2's do.
I am not completely useless.......I can always serve as a BAD example.