Well apologies for not responding sooner! Got the boat de-winterized and back to trying to fix this, and the seat-back cushion is now coming loose too. The plastic nipples shown above just go into holes in the plastic seat core (see pic attached). There are some scrapes in the plastic nipples on the headrest that make me think there was a metal clip attached with sharp teeth to keep it from coming out. Like a washer with teeth in the middle that I've seen in other applications with cars, but I wouldn't be able to attach it without getting to the back of the seat. Hopefully I don't have to take the whole thing apart to get there.