I’ve hit up support, but am writing here in case anyone has any ideas tonight.
The short of it is my print head is completely jammed on a piece of PLA filament. The little feeder gear ground a piece of filament to bits (and likely shoved all those bits down the hole). When I tried to pull it back out, the filament broke off in my hand, leaving only a tiny little nub (not big enough to grab).
I tried shoving it back down the hole, but it won’t budge. I tried removing the nozzle but that didn’t help either. By probing around, it seems like the jam is above the top of the hot end, but below the feeder hole.