The DHL guy finally came around 2 to drop off my laptop. They did not replace the logic board, but they did replace some audio components, the fans, some cabling and the latch for the screen. No shut downs after an hour, but shit does it run hot again. I suspect the innards are back to the pre-cooling adjustment state I fixed shortly after getting it.
I ran a 1080p movie trailer, full screen, and looped it for about a half hour just to give the CPU a work out. It got up to 160 degrees, which is within spec for the CPU, but it's so damn hot. The little strip between the keyboard and screen gets hot again, and the underside gets a little uncomfortable too. The fans never vary from 1,000 rpm, which seems so arbitrary.
But I suppose if I'm at the end result, that it doesn't shut down, then I can roll with the heat. The whine is still there, although subtle. I'm crossing my fingers that this is it though, as I miss being mobile. The repair work has a 90-day warranty, so I'll be working it out hard for the next month.
EDIT: I looked up in my disassembly manual to see that the sound hardware and power stuff are on a separate board together, and that's what they replaced. That instills confidence that the problem is fixed.