This doesn't sound like an Epic/CDC issue. This sounds like an insurance issue where they're not getting the medical coding they need. It's also possibly a hospital admin issue. Legally speaking, your doctors should be able to write a paper order for you to receive the vaccine (admin might disagree). Your medical coding experts in billing should be able to get you the required coding working with the insurance liason for the hospital.

Based on your definition of success, the paper orders fulfill that even if you don't get the coding and insurance coverage.