The situation here is not the driver stepping down after a minute.
It steps down randomly within 5 seconds. If I step it back up, maybe once, maybe a few times, it will then stay on high (600lm with the XP-L HI LED, less with the Nichia) until it gets hot.
I agree with moderator 007 that it must be the battery not providing enough power. In his case, the reason is the resistor mod, which drives the XP-L HI with more amps. In my case, it is the Nichia LED, which is obviously drawing a bit more power than the nominal 1.5A of the flashlight, enough to cause issues with normal 16340 batteries.
The way I see it, I either go for a vapcell, and keep the light as it is, or mod the R050 resistor to something with a bit higher value, to decrease the amps within the abilities of most 16340 batteries. I will try the vapcells first, as I prefer more output.
By the way, I did knock a couple of SMD components from their place while removing the black protective cap, but luckily I was able, with some effort, to solder them back on. I re-assembled the light and it works fine.