There’s a report of “one weird little trick” that apparently will allow you to continue this quest.
Yup. Get a haircut and you will apparently be able to continue the quest line. This doesn’t fix the rostrum not being usable the rest of the time, but it’s good enough for the quest. I guess.
It’s just a nonsensical workaround, but even if it’s stupid, if it gets you through, it might be enough for now.