I'm sorry it took so long to reply, apparently I'm not getting updates on posts :/
Screencap of the logs (Standalone is the top one). They don't show anything other than that they started (I verified the device settings in both remain unchanged from before immediately prior to the screenshot), but here you go.
Edit as writing: Thank you so much! It was an nVidia setting. No idea how or why it changed that, of all things, on a reinstall. I do now have a reoccurrence of one of the issues I reinstalled Windows for though, namely that the 4th card now runs constantly, and if I try to use it to render, my computer will crash with a DPC_Watchdog violation.
Basically (since I can't get an output due to a guaranteed, hard system crash when the issue occurs), if I open Daz Studio, and open the viewport, at some point, the system will crash. It can vary wildly (it has rendered up to 2000 s/px once), but will occur at some point, and usually instantly, even with an empty scene (only rendering the environment, for example). The only way to render within Daz Studio at all with all 4 cards "active/visible" is to soft disable cards 1 and 4 in the Device Settings. Prior to the windows reinstall (and I presume now likely to occur again since the symptoms are identical), this crash occurred in both the standalone and Daz Studio, whereas with the cards (for whatever reason) hard disabled for Daz Studio, I can render just fine with all four in the standalone. I will test this more thoroughly now that I know what setting got changed, but my best guess is somehow Daz Studio (ie. the plugin) is somehow confusing something, because it is the only program being open that forces this behavior.
Thanks again for at least getting me to open the thing I should have checked first!
Edit again, after a bit more fiddling:
Nevermind the second issue. Cycling Daz Studio twice, and doing a couple renders, the card is now behaving normally, and everything is stable. Would love to know what went wrong in the first place, but everything appears to be in working order now. Back to rendering normally (finally, almost a month later), I go!
Thanks again for the suggestions!