Welcome to FT!
I'm afraid you are 100% out of luck. There are no lie-flat options from Florida to Anchorage.
Air Canada is currently flying a Airbus 333 with lie-flat seats from FLL (Fort Lauderdale) to YYZ (Toronto). From there you can get to YVR (Vancouver) on AC which has (on selected flights) lie-flat seats. From YVR you will have to make do sitting upright. I doubt the connections will work in your favour, but give it a try on
www.aircanada.com