I'd probably rent to #4 and maybe 5-6 if they had a landlord reference that the animal isn't harmful to property. 

I do not want to harm my tenant.

No harm done.The LLC will not be able to obtain a “certificate of good standing” from New York’s Department of State.

You would have to prove that the toxins were still in the air.

I highly doubt that they would make the effort to come back and do something that would harm the property, but it doesn't hurt to be sure. 

If your tenant, or their guests (which may include children) or their dog, is harmed by a wild animal with sharp pointy teeth living under the deck with its growing babies, that they informed you of and asked you to get rid of - then I see "liability" on a neon sign hanging above your head.Use your common sense here, instead of looking for some technical loophole.  

I prefer my occult gatherings to be in a field with white maxi dresses and long dining tables, but really, what's the harm in people letting loose in the name of knowing t h e m s e l v e s? 

I always embed hardware cloth into the hole for good measure before foaming it.If you catch one in a glue board, you can use vegetable oil to free it once outside without harming it.I've always used the snap traps with PB as @Victor S. suggests, but the most important thing is to find their means of access and block that. 

No harm done.

And, while that might have been worth discussing had they approached you as "adults," they chose to financially harm you.