Airbnb eventually offered me around $250 out of $763 of damages. They gave me 48 hours to accept this amount. I wrote back stating that it was $763 worth of damages and that they should reconsider this amount.
After not hearing back from them within that 48 hours, I contacted them again to ask what was happening. They responded by saying that they had withdrawn the 'offer', as I had not accepted it within those 48 hours. They were not willing to talk to me again about it and said that I should take out landlord's insurance.
So ... I received $0 damages payout.
Once bitten, twice shy. I am now really selective in whom I accept as a guest. They have to have at least one positive review from another host, have been a member for a while and have at least 4 verifications. I also ask them to tell me about themselves and why they want to stay at my place.
This has meant that I have declined more guests than accepted. But at least I believe that my guests will treat my place with respect.