Perhaps their lease term isn't up or maybe they were not given proper notice to end their tenancy.

Water damage never happens in small amounts, until its noticed and by that point it's typically a larger job than $1200. 

Which in NY means like 3 months of notices and then a court case and an additional two weeks past that even if you win. 

What is the best way to give notice and what is a reasonable amount of time? 

The issue is giving value/service by virtue of honesty, and getting confronted by that.The problem that I notice is people get very offended when they don't hear what they want to hear.

They would also allow you to modify the rental agreement with only 30 days notice.

You should notice I didn't say "Positive Review" or "Great Review" - this is critical to the psychology of such statement.Overall, the key to using cash for keys successfully with a stubborn tenant is to approach the process with empathy and open communication.

I would like to be able to occupy the property for 1 week every 4-6 months, which they agree to (with enough notice on dates) as they have to travel for work at times and could easily vacate during these periods.Has anyone written this sort of agreement into a lease?

Do you have collected any certified letters of tax notices sent by the local tax collector?

Remedy after termination.If the rental agreement is terminated, the landlord may have a claim for possession and for rent and a separate claim for actual damages for breach of the rental agreement, reasonable attorney fees as provided in § 55.1-1245, and the cost of service of any notice under § 55.1-1245 or 55.1-1415 or process by a sheriff or private process server, which cost shall not exceed the amount authorized by § 55.1-1247, and such claims may be enforced, without limitation, by initiating an action for unlawful entry or detainer.