I checked in Task Manager, and the game's still using CPU, memory and disk, so i know it's not a complete lost cause
(10.2% CPU, 1047.2 MB of memory, and 0.1 MB per second in the disk at first, and then recently it changed to 12.1% CPU, 921 MB of memory, and 0.1 MB per second in the disk)
I've kind of resigned myself to waiting at this point, but is there anything else I can do to make sure I don't lose the household I've been working on?

bad custom contents, perhaps? try running the game once on a fresh install, ie; rename your current The Sims 3 folder to something The Sims 3 - Backup, then load the game and see whether it fixes your relationship screen problem.