Ok, I looked at the final link you posted. It says the driver is 10 x 20mm. You said you measured 30mm. That has to be the whole housing. I removed the back of 3 AixiZ housings, like you show in the picture with the driver in it. From the face to the inside back on mine is 21.65mm. The threads are just over 3mm. So, your 20mm module is abt 1.5 mm past where the threads start down in the housing. My numbers indicate what your picture shows. The link pic does show a snap off tab at the bottom that should solve that distance. The area where there are no parts and indents on the sides with awhite line across it. You said it was already snapped? If it's like the pic and that one is 20mm , when you snap it it should drop in just below the threads.
Ok, if it doesn't, you have 3 choices IMO:
1. Use an emery board and take abt a 1/16" off each end. Looks like it can be done easily and it fits.
2. Drill out the back it fits.
3. Buy a smaller driver. The rckstr was mentioned. It fits.
I don't want you troubled anymore but did you read the description compared to what is on the picture?
The description says 80-400ma, advertised(title) as 80-500ma.
Also, description says 0V off @ >2.5V laser on, pic says TTL+ 0vDC = Beam on, 5VDC = Beam off.
I hope this doesn't cause you anymore confusion.
Appreciate the link. They had a deal on 2 for $8 shipped. So I bought 2. I'm new too so I can always use a couple low power adjustable drivers starting out. Hard to build an LM317 for that price.