Wow! Shocking to a northerner like me to see that water temps in two separate Florida locations drop down near 50F at any point in the year.
If you look at a range map showing the historical or even current range of the species, you see Alligator Gar ranging much further north than Florida, so it seems reasonable to assume that they are capable of withstanding much larger seasonal variations...in particular, considerably colder minimum temperatures...than those Florida charts indicate. Of course, the origin site of the fish you actually obtain will have a bearing on how adaptable those particular individuals would be. Also, being adapted to "survive" a given low temperature limit does not mean that they could necessarily thrive or even survive if the low temperature persists for an extended period of time.
Interesting thread, looking forward to how it develops.