Tenant removal after lease expiration?

I have a rental property in Lee County, Fl. My renters were on a month-to-month rental agreement, with a clause in the agreement that if I sell the property they'll have 30 days notice to move. They're consistently late on rent, (currently two weeks behind), and instead of filing an eviction, I've found a buyer. I'm notifying them by Fed Ex, certified letter, emails, text, and posting a notice on the property. My question is what are my rights if they're not out in 30 days. Do I still have to file an eviction anyway, or can a sheriff look at the proof of notification and the agreement, and make them leave my property? If it's not as easy as a sheriff, is it possible to get a writ of possession without the cost and time involved of filing a court case? Any advice from knowledgeable or experienced property managers would be very much appreciated. Thanks