Welp, guess I'm just waiting for my new RAM to ship then. Thanks for the info - will update when I have all my parts. Crossing my fingers in hopes it's not the mobo.
Ooookay. Seems everything is fine now. Installed an entirely new brand of ram - 16 GB again - and everything has been running smooth as a dream. Hard to believe every stick of RAM I bought out of 4 was bad... Ah well. Thanks both of you for your help, I would have never guessed it was the RAM to begin with. o.o