Yes it would be easy, if we had planned for it ahead of time. Antibodies fade over time, so you can't do an antibody test much later. And neither antibody or viral tests would have been guarded for anti-spoofing or external verification. Some people may have just gotten a text or phone call from their health care provider, or used a self administered test.

Studies have shown the common (LFIA) antibody tests administered to most people have specificity <50%

Which ones? I'm looking at this page and am seeing numbers in the high 90's https://www.fda.gov/medical-devices/coronavirus-disease-2019...

Those are not LFIA tests

Seems like in the context of this use case, the medical community would adopt the tests with the higher specificity, and there would be market pressure to lower the cost, if needed. Seems a bit of a reach to point to tests used for use case A to discount use case B.

Yes, it is possible to accurately detect antibodies with certain antibody tests (primarily, blood draws) administered by certain parties. But now you have a complex patchwork of antibody test exception standards formulated and enforced to satisfy the preferences of a small number of individuals, most of whom simply object to vaccination on ideological grounds. These folks should just get vaccinated.