Cash for keys usually works out very well for both the tenant and the bank. However, you can probably dig your heels in and make them give you a 60 day notice. But, again, legal counsel is the way to go here!
This sounds pretty serious. You will want to contact a competant real estate attorney ASAP. These situations are too intricate for an agent to be able to answer on a message board. You need legal help and unfortunately realtors are forbidden from giving legal advice. I know you were hoping for a quick and free answer, but I don't think there is for you in this case.