Adam,
There are three classes of wildlife recognized in Florida's laws. The American Alligator lands in Class III, and may be owned for exhibition or sale only, without the 1000 hour experience requirement.
Class II crocodilians consist of all caimans (except the Black Caiman)and also the Chinese Alligator and Dwarf Crocodile.
All other crocodilians are in Class I(You'll notice that the most dangerous and largest crocs, besides the American Alligator, are listed in Class I).
If you worked at Busch Gardens and any other zoological-related facility, and if you can get at least two of your former superiors there to write letters confirming your 1000 hours of experience for EACH class of crocodilians, and they and you can detail the extent and details of your experience, you have a good chance at getting a permit. The Florida Fish and Wildlife Conservation Commission is cracking down on possession of wildlife, and if your experience was in the too-distant past, you may well NOT be granted the license for Class I or II.
Go here to research: http://myfwc.com/permits/#Wildlife
Hope this helps.