Just to see if it worked, I tried measuring the path length between the laser tube exit and various spots on the platform with a laser distance measuring tool / rangefinder:

That is a reenactment based on actual events.
The trick is to put a retroreflective panel at the tube exit:

The key under the tube comes from the key switch on the front panel, which is locked in the OFF position. That way, I can’t fire the CO₂ laser without opening the rear hatch to retrieve the key, whereupon I’ll most likely notice the retroreflective target I forgot earlier.
Protip: Always set things up so you must make two mistakes before the bad thing happens. I’m certain to make one mistake, but I can generally catch myself before making the second mistake.
Then it’s just a matter of positioning the base of the rangefinder on the laser head and convincing the targeting dot to go backward through the mirrors to the retroreflector:

Which is a reenactment with a laser pointer through Mirror 2 to Mirror 1 to the reflector. If I had a few more hands, this stuff would be way easier.
Then drive the laser head around the platform and make measurements:

The distances down the left side are at the Mirror 2 entrance aperture, the rest are at the Mirror 3 entrance on the laser head. I think the measurements are within ±50 mm of the “true” path length at any given spot, because I did not jog the head to exact coordinates. The two values in the front right corner suggest ±10 mm repeatability with my slack process and cross-checking the various differences along the axes comes out reasonably close.
Don’t believe all the digits.
Doing this for real would involve figuring the offset from the Mirror 3 entrance to the HLP-200B Laser Power Meter target, then positioning the rangefinder at that point:

My rangefinder (an ancient Bosch GLR_225) can use four different measurement origins; I used the default “end of the case” setting, put that end flush-ish against the mirror entrance aperture, and declared it Good Enough™.
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[…] Having measured the path lengths, set the laser pulse power to 25%, then plotted the power measurements against path length: […]