Update: I did end up completely wiping my boot drive (and my "gaming" drive, just in case) and reinstalling everything from the OS on up. Also opened the case and checked connections and gave everything a good dust-off, altho there really wasn't much to clean off. I also removed the heatsink/fan from the CPU and cleaned that and put new thermal paste down to reseat it.
Anyhoo what with one thing and another (not to mention all the hours and hours it took to get everything reinstalled) I didn't get a chance to play the game at all until this past weekend, but I've played several times - in one instance for 4-5 hours straight - without any issues at all.
I'm still thinking it was an issue with the graphics drivers not updating/uninstalling properly, as I had THREE entries in the registry for three different versions of the same graphics driver. I think they even reappeared after I tried to manually delete them so something there just wasn't right. After the clean reinstall, there's only one entry for the current and correct version.
But whatevs, everything's running faster and cleaner now all around and Skyrim isn't crashing my whole system so I'm happy.
