So I broke this down (and I'm mostly just live-blogging this in case anyone ever needs this information again).
I found the culprit - there's a flange that is supposed to basically push the gear that corresponds to the take-up spool. There was a line of wire that was holding it inward - it needs room to move, but it won't work if it falls out of alignment. The wire was off and loose in the bottom and was too short and had no looped or hooked ends - I think it just disintegrated basically.
I image-stabilized this because I did not feel like getting my partner or a tripod and the video was wonky. But you can see how it displaces.
https://streamable.com/6lh87c
Unfortunately, I don't entirely know how to remedy this. Firstly, I don't even know where the wire attaches to. It ostensibly goes around the pin on the underside in the second image, but the back end is a mystery. I could probably use some sort of epoxy and a sliver or something and attach it to the outer edge of the disc. Unfortunately there's nothing to be cannibalized from my Petri S7 which is significantly different in design. So my options are to:
A. DIY a solution to hold that in place so it doesn't flop all over but that will certainly nuke it for the future
B. Only shoot in one specific portrait mode