Welcome to Cruise-Chat. A four hour window of time for an inbound flight would be far too close. But for an outbound flight I think you should be okay with 4 hours since the Miami airport is only 8 miles from the pier. If it were me, I'd book the low cost flight at 11:00am. Just be sure and bring a copy of your flight itin and provide it to the Pursers Desk and ask for "Priority Disembarkation". They should be able to get you off quicker that way.
If you really want to be safe and don't mind toting your own bags, you can self disembark. Just let them know you'll carry you own bags and don't put them out the night before. When they begin the process you just get off with your bags and grab a cab.