Replying to my own post for future reference. Further research on the medical - it seems Citymed Auckland charge standard rates for vaccines. Might as well just let them do it. Traveling to the US - Yes, it is possible. Immigrant lawyer said no worries. I went and US immigration didn't care at all. Currently coming back 1 week before my medical in NZ. So I got Documentarily Qualified on the 19/05/2023, received NVC email on the 31/08/2023, for an interview set for the 13/10/2023.