He always paid on time, didn't destroy anything, left the place spotless, but when it came time to do showings he put up a fuss.

I have one Labradoodle, and she has already destroyed several pairs of shoes and books, and started a fire.

Then, when you have to say no, they take it personally, as if their best friend just destroyed the friendship.I had to stop befriending my tenants because of this.  

This is a difficult situation all around and I don’t envy your situation....The fact remains that life happens and you can’t let things out of your control destroy your rental returns.

You have a tenant you like, who respects your property and pets that don't destroy anything.

Last thing you want is for a disgruntled tenanted to destroy your rental all because you wouldn’t let them break the lease.

Service animals are very smart and highly trained and the odds of a service animal destroying your property are slim to none.

And denying him the right to chop down the oleanders will destroy his flower shop business?

If you are worried she will destroy the house on the way out offer cash for keys. 

If they have been homeowners they are pretty low risk to destroy the house or not pay; the bigger risk might be that they move soon (that it is a transition home rather than long term).If they are an applicant who has never lived away from his parents, this is a high risk applicant.