UPDATE: Well, I managed to upload the new firmware using the CMS tool. It took no more than about 5 minutes total. The basic camera settings (OSD date/time, etc) were all reset, but the IP/port configuration I'd initially set did not change. I verified that the version on the camera matched the .bin I installed.
Unfortunately, the dimming/brightening phenomenon was still happening - albeit, much slower, and less frequently. Though, that may be because of the time of day. During my initial discovery of the problem, it was mid-day, on a very sunny day. Today, while still sunny, it was around 4pm - and not as bright.
I've sent another message to the seller to let them know the problem is still present.
UPDATE 2:
Seller responded that I should tick the "anti-flicker" box on the camera parms. Pretty sure I tried that already, but I'll give it another go.
While comparing the settings to the working camera tonight, I noticed a constant toggle between day and night mode:
I don't know if this problem existed before the firmware update. I'd have to connect one of the other two remaining (non-updated) cameras to verify. Either way, this is giving me a sinking feeling.