Okay, I know I am going to get a lot of flak for writing this, but perhaps the simplest and best way to handle this is to just lie and say you got the vax.
We should have no compunction to lying to people who support liars.
It gets them off our backs.
It messes with their numbers.
We get “marked down” as having been vaxxed and that might buy us some time.
No need to lie.
Just close the door.
Because they have a list of who HAS gotten the shot...if you’re not on it THEY KNOW.
They will violate HIPLAAl laws, to illegally get your medical records. They will know.