Hmm, it’s starting to come together now. A little.
I’ve only skimmed the first page of that thread once or twice. At your suggestion I read the entire thing. Lambda doesn’t say that it’s voltage-controlled, but it is. 331C1 is a voltage controlled (CV) boost controller for 3.3v. I have been unable to find a datasheet, but 501C1 also exists (5v instead of 3.3v). Here is a clear photo of 501C1 from this thread on elektroda.pl. I see some more discussion on 501C1 over in this thread on the same forum.
Voltage controlled seems to be able to work acceptably, at least in some cases. DerWitchel also used CV in a driver (step-down though) for SST50/SST90.
In this case we’d see a little lower current on XM-L2 or a very low (<2A) current on XP-G2, based on djozz’s charts (post #51). Of course MT-G2 or strings of LEDs are both completely out of the picture, but that was really true anyway on 2s1p NiMH - regardless of driver selection!
It would still be worthwhile to me to find out exactly how this driver operates, but I don’t think that actually cloning it will produce great results.