as an alternative to testing weekly or proof of vaccine, you should be able to provide proof that you have had a positive test in the past. Reinfection rates are fairly low.
I'm not sure there's a good test to prove you've had covid previously if it was a while ago, antibody blood serum levels dissipate in 2-3 months from the studies I've looked at.
Also reasonable, and I'd tend to agree. Per some type of medical confirmation of course.
I am going to take a wild hunch however that many would object to disclosing any such proof also. A certain % is that dug in.