Sorry for the long wait. It seems the motherboard was indeed faulty (it took a while for the shop to verify this, but evidentially they also got freezes with parts of their own on my mobo). I now have a new motherboard, so here's hoping that'll be enough, rather than finding out there were several issues and not only the motherboard. If my system survives the next 24 hours without problems, I'll consider this solved ^^
As for the CPU, it was a weak one from someone who's into servers. It ran fine on a smaller board, but that one wouldn't be able to handle my CPU or something like that, so I couldn't test that way.
I had updated pretty much all drivers in Windows, but beyond that, I only updated BIOS and SSD firmware. I had pretty much eliminated GFX card as being the (only) problem, though, by taking it out for a bit.