Can I get medical with a different AME after being deferred?

So foolish me went to my medical totally unprepared thought it will be straight and easy. Got deferred by the AME for some trivial issue. Later I figured out with another AME that this is a "issue and FAA will ask you for more info" situation, or could even have been a straight forward issuance.

Regardless, now Oklahoma has my papers and it has been close to 3 months with no update. Called Oklahoma and RFS and no success.

My question is, if a different AME is comfortable clearing me, can I just repeat medical with him, while the previous one is pending and who knows how long FAA will take.