I can't speak to Drones, but be warned, Antigua is NOT a Bahama;s or Jamaica, its been 3 years since we rented a condo there, beautiful country, rainforest trip was awesome, BUT, they are not , how shall I say- Quite "tourist ready" like other southern escapes. Took us 3 hrs after arriving to check into our condo, almost the whole first day in renting a car!
Wait in front of your condo sir, then, go to Jolly what;s s name hotel,(parent co.) car at front desk, wait at front desk, 3 hrs.)NO, go back to your condo, this went on till suppertime. Off to rainforest, wonderful, return to car, flat tire & no spare. Called car rental -Closed till next morning, Thankfully, another quest in parking lot, his car won't start, gave us his spare.
I drive family back to hotel, then return to pick up "spare" family & drive them to hotel . Day 2 over.
DO keep cash in your pocket, seems to get things done much quicker., yes, I was speeding(no posted speed limit signs) back to hotel trying to at least sit poolside before sunset, Officer, here's my ID, no, that 20 Am. isn't mine, must be yours.
Not much help with drone travels I know, but, so many unknowns & confusion I would try & get some definite answers as to their policies. Cash certainly helps expidite things, which always makes me nervous as to the local rules, laws or lack of them