Have you tried feliway or rescue remedy.
You might want to check if there is a Mobil vet in you area who can come to your home.
If not, ask your vet to prescribe a mild tranquilizer before taking them in for shots.
They are both very beautiful and I think it’s great that they get along so well with your other pets.
After 12 years my black cat still runs from me when she feels like I’m trying to pick her up. It took lots if time and much patience but she is letting me pet her now.
I wish you the best of luck.