I believe I've found the cause of the flickering I mentioned when on battery. It seems I was right, it was a power-saving issue, though not a direct problem with TLP or any other power management suite.
I didn't realize my system's chipset was Skylake, which still isn't entirely bug-free on Linux, it seems. The Arch wiki suggests two solutions to various GPU issues, disabling hardware acceleration, and disabling rc6 power saving. I didn't even try disabling hardware acceleration, because I want hardware acceleration, but disabling the power saving I did try.
It seems to have worked and totally stopped the flickering, which must have been sub-second GPU hangs.
Unfortunately, however, it nearly doubles my power consumption. I think I can deal with the flickering for now, hopefully some progress with the drivers is made soon.