Well I just got off the phone with United, having read them the new ticket number, and they said there is no record in their system of that ticket number. Instead, I apparently have 3 separate PNRs in their system, one that is showing as unpaid and missing a segment, and the other two with no valid ticket attached. They said I'd need to talk to Turkish and that there's nothing they can do.
So I guess I fill out the feedback form again? Kind of feels like I'm stuck in an infinite loop at this point. Clearly Turkish isn't pushing the new tickets to United's system, whatever they're doing.