As you have already found, Laser won't work as the cross section of the line melted into the surface is not correct for subsequent fracture of the glass.
The diamond drag system works extremely well. I have found that the surface of the glass needs to be completely clean (no fingerprints) for best results and the glass breaks cleanly.
Obviously the edges of the glass are very sharp but this can be reduced by rubbing with a small oil stone if necessary.
Because there is some (quite small) resistance to movement with this process the CNC machine need to be reasonably good quality and rigid.