So I tried searching for, "hitch," "hitching," "feeze," and "freezing," and all I could find that accurately described my problems were
this post, which is nearly exactly my problem, and
this ancient thread which isn't really my problem and has already seen Pescado say he cannot replicate the bug.
To give as much information as I can, I own TS3, Ambitions, Late Night, Generations, Showtime, and Supernatural only. No stuff packs, none of the other expansions. I'm using the most recent AM at the time of this posting (1.48). I have absolutely NO CC. This is as close to a vanilla install as I think I can have.
System specs are: Intel i5 2500K (base clock), nVidia GTX 560, 8GB RAM.
What happens is that after a few days of playing in-game, the game starts doing this weird little time-freeze thing where everything in the simulation freezes. The clock stops, animations stop, inactive sims stop, I cannot move the camera, and I cannot click on anything. After about thirty seconds to a minute, sometimes longer, the game will just pop back into place and everything resumes like normal. It doesn't happen at 1AM (I don't know what 1AM has to do with anything but I did see that there were several mentions of an infamous 1AM freeze), and though it DID happen during a carpool, it happens at all times of day, even when my sim is sleeping. However, while all this is frozen, things like the plumbob, sleep 'z's, and fountains continue doing their animation, so the game hasn't hardlocked. I can move the cursor around but it does not change shape based on what I mouse over. I madly clicked a few times and it seemed to queue up the clicks, causing it to instantaneously navigate my sim's interaction menu when the game resumed.
Also as a small symptom, clock time is no longer regular. It's jittery and uneven, so sometimes the game clock goes (for example) 1 real second = 1 game minute and sometimes it'll be 3 real seconds = 1 game minute.
I have not had any of the other bugs mentioned in that thread earlier like a Sim just freezing mid-stride and the clock going on, or actions taking FAR longer than they should (other than the waiting to shower thing, which was described as loading an outfit in and not doing it quickly).
This did end up in a stoppage of time that never recovered and I had to force-close last night after waiting a few minutes, but the program itself never actually crashed.
I can upload a save if need be (if someone will tell me which files I need to upload) and if anyone can think of any additional information that would be useful I'll post it up.