Ah that could definitely cause some confusion. He was attempting to mod the driver by adding a 7135. But you are correct on all points. I’ll take a look to see if I can find which boost ic the driver uses.
I’ve been curious as to the fluctuations as well, although mine do it on alkalines and eneloops.
edit
Here is a photo of the driver. I haven’t been able to identify the crucial part in the middle that appears to be marked “J2NL” which is the boost converter, presumably similar to the “CFC2S” found on the nanjg 110