We began by measuring our cardboard thickness. While measurements varied slightly depending on the piece of cardboard, all hovered around 0.151" +/- ~0.007". We created a comb cut file with slot sizes of 0.145", 0.148", 0.151", and 0.154". We also tested the laser kerf by cutting a small square; while measurements were consistent, it appears that the kerf is slightly different in each direction: more material is removed when cutting vertically than when cutting horizontally - roughly 0.010" when measured across the vertical axis, and 0.012" when measured across the horizontal axis.
That said, cardboard is rather forgiving at these tolerances, and while joining the two 0.154" slots felt smoother than we liked for press-fit, all of the other slot dimensions were easy to join and held their place reasonably well. I settled on a slot width of 0.148" for my project, which worked well.
As for laser settings, we settled on a speed of 300 (out of 500) and a power of Full Power. Evidently, Full Power is in fact different from 100% power on our machine - while Full Power at 300 speed cut through nicely, 100% power at 300 speed did not (see images below).