So I don't want to jinx myself but I think I found the culprit. As I suspected, the flickering appears to be hardware related. Indications of such include --
1. An otherwise fine little Mini PC was suddenly on the blink, literally.
2. Software fixes (reinstalling the OS, turning off certain older softwares) would fix... then unfix themselves.
3. The flickering wasn't consistent. Sometimes it would go away for hours, but other times come back.
I had already tried unplugging everything, waiting a few minutes, plugging it back in. But the flickering came back. And then I noticed something too stupid to be true. See this quality plug strip --
When I first unplugged that strip from the wall I also unplugged everything plugged into it. Full paranoia. That was a few days ago. Today I decided to try again, and I noticed this --
Do you see in the first picture how you basically can't see it? In my dim living room it was as invisible. But today I noticed it and pulled the plug strip closer... only to learn... it appeared to be the littlest bit loose. This is the LG TV's plug.
This confuses me because previously I had already tested the set itself, which I almost never watch as a TV. For an hour or so it played perfectly with no flickering. So I had ruled the set out.
But maybe when the PC tried to work with the TV there wasn't enough juice for the TV somehow?
Not throwing myself a victory parade yet but a loose plug is a loose plug.