Okay, trying to see if I can reproduce it with an almost-empty cell.
Drained a 30Q cell to 3.0v. Popped it in the SC600w MkIV HI. Turned on H1. Light goes to full output for a couple of seconds, then steps down to medium. Normal behavior.
I tried letting it run for awhile, to get the cell down close to the ~2.7v LVP cut-off. I got bored, so instead froze the light for 1 hour in the freezer.
From frozen, turning on H1 causes it to struggle a bit to maintain full brightness for a second or two, then goes to medium briefly, then low. Normal behavior.
After it warms up for a few minutes, it can now maintain medium again. But no sign of "shut off from H1".
Okay, now I'll start the long process of just letting it run down the battery until it shuts off. This will likely take many hours, as it happily sips juice when it eventually settles down at a very low output. Hopefully, after that, the cell will rebound just enough to let me turn it on to H1, then I'll see if the behavior is similar to the bug I've seen.
The behavior of the bug is a little weird. It doesn't actually shut off the driver. When it "turns off from H1", it really just cuts power to the LED. Clicking the button once again, actually shuts off the driver like you normally do when shutting off the light. You have to click again to turn the light back on. Or, you can double-click after it "turns off from H1", and it will turn on to H2. So the driver appears to think it's still turned on in H1, even though there's no light coming out.
I'm not sure if that's the expected behavior that happens when the LVP kicks in at around 2.7v. I guess I'll find out... eventually. If I can turn the light back on after LVP kicks in, that is.