UPDATE 2:
At home again tonight, I tried it on IE 10, and it worked correctly. So clearly the issue has to do with something browser-related. I would suspect cookies (as I’ve never used IE to view the site before now), but as said in the OP, I had cleared out cookies before. Will try another clear out again before crying.
ETA: Nope, no luck. Commencing crying.
PLEASE if you have any ideas, I’d appreciate them!