You write a nice letter for your congressional/senator's immigration aide, detailing all the info you have and providing copies of evidence you have (DS-3025, CDC info on vaccines, that chart above showing it's not age appropriate). Then you ask assistance from them to get in touch with USCIS office that has your case (field office, where did the denial letter come from?) and ask them to reopen the case on the basis of misapplication of medical basis rules on vaccination in adjudication of AOS.
If your congressional/senator's immigration aide office is nearby, you go there in person (schedule an appointment ahead of time in case they don't accept walk-ins) - if not, email should suffice and then you can follow up with a phone call. When I had a USCIS issue (non-production of green card post POE), I handled it all via email.