They are just required to use due diligence and use judgement to make sure they are sending to the correct address.

You won't get anywhere with a suit, even if you were successful, forcing them to pay will be almost impossible... yes you can place the judgement notice on their credit and keep renewing it every 5 years but that rarely breaks out the checkbook.The short term rental is going to be hard to lease; and it's clear your vacating tenant understands that. 

At some point, across the street it isn't raining...and the storm is moving. 

The lender would have to pursue and obtain a defiency judgement for the unpaid balance of the loan, after foreclosure.

(I had some judgements against me, which has since been taken care of, but my credit score remains incredibly low.

every state is different but in Florida your primary residence is judgement proof.

Guests above create a water leak situation that rains down on your guests.

Making judgements to which business the Communications Decency Act applies or doesn't is far outside my legal education so I'll refrain from commenting. 

Definitely get that judgement and get collections on it - it will stay on her credit report. 

If you have a judgement is better but they will work with anything (lease, ledger).