After appearing on the HAD blog, someone IM'd me and suggested to check how snugly the lens was seated and... It was a loose lens!

The lens retaining ring had come loose, and slowly unscrewed itself down the lens tube so that the lens was simply laying on top of the ring. Individual pulses of air caused the lens to jump up, changing the focus and the cut width!

The retaining ring was waaaay down the tube - more than 10 turns away from snug.

I'll need some way to permanently set the ring so that it doesn't come loose again.

Update:

Looking at the CloudRay store on Amazon, the retaining ring has a plastic washer to protect the lens. They also sell silicone rings to isolate the mirror from the retaining ring. These probably form a locktite interface with the lens.

My own cheap chinese laser cutter has no such padding - it's a metal ring that presses directly onto the (glass, fragile) lens.