Meno
I’m not sure the answer to your question (Its a good one)
a related (strictly hypothetical) question would be is it muttar/appropriate for the administrators of the vaccine to let you cut the line ? help you cut the line?
This seems like less of a question to me. For YOU to cut you can argue chayecha kodem, you come first and if there are limited vaccines, you want to take care of yourself, a principal that certainly has basis in halacha (Though I’m not saying that would be the final decision in your hypothetical case just that there is a legitimate discussion) for them to help you or even let you cut seems less justifiable
(None of this comment is directly related to the subject of the OP whci his not really described in Meno’s question