Thanks, Strypes! That's a good idea, but it didn't work, largely because I'm an idiot.
I deleted both my "thumbnail cache" and "thumbnail data" files. On the timeline clips, both before and after deleting the caches, the thumbnails turn up perfectly fine and visible.
While poking through the timeline, I zoomed out and re-scaled my track sizes to the smallest width. This revealed a massive, media offline reference clip about 6 video tracks above what my timeline was showing. Hadn't even dawned on me that there could be another clip floating above everything that was offline.
Delete that, and voila! Everything is lovely. D'OH!
Palm, meet forehead.