All the ideas above sound appealing off the cuff, but some of them could get you sued, and the tenant (or FHA) would win.
You can't charge a pet fee for a service animal or assistance animal, and you can't demand a doctor's note to prove the need except under certain specific circumstances.
It is complicated and painful reading, but any landlord needs to read the publication below before responding to one of these requests or asking for any "proof" of need:
https://www.hud.gov/sites/dfiles/PA/...C1-28-2020.pdf
Here's some additional info that briefly touches on service animals:
https://www.hud.gov/sites/documents/huddojstatement.pdf
And if in doubt, hire a lawyer to give you legal advice!
Don't shoot the messenger. I don't agree with these rules because they are too easy for scammers to abuse. But no one asked for my input when they wrote the rules! So .....