1. Lower your maximum guests. Do you really want that many people? And why?
I have 3 bedrooms and we are allowed 7 by the city but I set it at five to accommodate families. I mostly get groups of four or less so I charge extra for a fifth person and turn down requests for more than that. Same revenue, less wear and tear on your property.
2. Some people enroll in Airbnb via Facebook so see if you can find research new guests.
3. Make it clear in your welcome note that ONLY guests listed on the reservation may visit without prior approval.
4. My house rules state damage is billed at replacement cost. If they stay they agree to the rules.
5. I tell people without prior review to contact me before booking. All guests are asked to tell me a bit about themselves and why they are coming to town.
6, I only allow locals in rare situations.
and definitely yes to two night minimum.
I think the problem is Airbnb has really set the bar low for guests.