Having established that the RMS value of the huge current spikes at low PWM settings doesn’t amount to anything meaningful, I cranked the AM502 current amp gain to 10 mV/div, re-ran the tests for PWM values from 10% through 99%, and recorded the RMS value of a single line through a square of the same pattern:
Each square is 1 mm on a side and the pattern runs at 250 mm/s, so the laser will be enabled for 4 ms. For example, the test setup shows the result of a pass at 50% PWM:
The two cursors mark the duration of one block, with the laser current in the bottom trace starting off with the usual off-screen spikes, then settling down to a constant-ish 13-ish mA for the rest of the block. The 13.74 mARMS value (the AM502’s 10 mA/div matches the scope’s 10 mV/div, so you can read mV as mA) includes some part of those spikes (the higher gain clips the tips), but most of it comes from the stable-ish portion.
The whole measurement set as a slide show for your amusement:
Tube Current – 10pct – RMS pulse – 250mm-s – 10ma-div 
Tube Current – 20pct – RMS pulse – 250mm-s – 10ma-div 
Tube Current – 30pct – RMS pulse – 250mm-s – 10ma-div 
Tube Current – 40pct – RMS pulse – 250mm-s – 10ma-div Tube Current – 50pct – RMS pulse – 250mm-s – 10ma-div 
Tube Current – 60pct – RMS pulse – 250mm-s – 10ma-div 
Tube Current – 70pct – RMS pulse – 250mm-s – 10ma-div 
Tube Current – 80pct – RMS pulse – 250mm-s – 10ma-div 
Tube Current – 90pct – RMS pulse – 250mm-s – 10ma-div 
Tube Current – 99pct – RMS pulse – 250mm-s – 10ma-div
When confronted with data points, plot them:
Huh.
I expected the line to pass through the origin, which it most certainly does not. One could make up a story about how the 30% and 40% PWM points are Close Enough to the line to sorta pull the bottom end over to the left a little, but even that doesn’t explain the known-to-be-weird results below 30% PWM.
A better story might be that 30-ish% PWM produces the minimum current required to fire the laser tube. Operating below that current works, in the sense that the laser produces a beam, but it’s out of spec. Running above that current eventually lets the power supply reach an agreement with the tube as to the operating point.
As before, those measurements do not account for the reasonably consistent results of scorching some cardboard:
Cardboard is not the best test medium and I now agree RMS isn’t the best measurement.
More study is indicated …
The Smell of Molten Projects in the Morning 
In semiconductor lasers the device will draw current and emit light before you hit the threshold where coherent light (lasing) happens. Maybe something similar is happening below here below 30%?
The tube is definitely firing at 10% PWM, as shown by the target, and emitting a tight beam, but it may be firing intermittently (with each spike) or erratically (when enough spikes happen). It definitely hasn’t settled into the continuous-current mode seen at higher PWM values.
Perhaps you know: do diode lasers run at a constant (ideal-ish) current modulated by PWM, rather than by adjusting an analog current to change the power output? Given what little I know of diode lasers, there’s such a fine line between lasing and burning up that I’d definitely set the current once and be done with it, but that’s just me.
For sure, you are right about the thin operating margin. For the low power devices I used, the onset of lasing was 10 or 20mA, the max was 100 mA IIRC and heat had to be managed carefully. Net result, the dynamic range was low, and you had to carefully calibrate min and max current. PWM is the best approach to managing power if your application permits.