I’d be giving them the do it the day before or not at all option and stare them down.
I havent had half the needles you have but I’m still scarred mentally after my port insertion there would be no way they would be getting the rest of that done.
Do you have a support person that could advocate ie stress how much of a mind mess this is for you, that you could get to help convince the medical team? Btw the medical team sound like they need bedside manner training for dismissing your fears. Perhaps that is the second option complain about the dismissal of your concerns