Cash-for-Keys may be a viable option if they'll cooperate. I handle Cash-for-Keys for several banks so if you need some advice as to how to write up the contract and conduct the inspection, please let me know. If you're not willing to pay the amount they want, then I would start the eviction process right away in order to protect yourself. The tenants have not been honorable in their past dealings so they may be troublesome even with the Cash-for-Keys.
You can start the listing process now, however it will be much smoother if the tenants are out.
Again, please let me know if you need advice and help with the Cash-for-Keys contract. Good luck!
Realtor - Certified Preforeclosure Specialist - SSIC
Keller Williams Realty