The line to clear security is by the worse in Miami than anywhere in the world we have been. Last time we had a TSA guy for some reason come up to us out of the hundreds in line and tell us to go down a gate or two. Well I had been teasing him. The line there was only 20 or so people long.
If you are leaving Houston at 3:50, it is a 2 or 2 1/2 hr flight to Belize City. You will arrive too late for a connecting flight or a water taxi, I'm pretty sure.
If you book onto a Tropic flight so that they know you're coming, they will often hold back a plane for you. No guarantees, but it's happened for me and for others I know. Only Tropic, and must be pre-booked. My record is landing at SP after 8pm!
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