I live in Alabama and buy long guns in Florida and Mississippi. No problem.
I can buy pistols also but they are sent to a FFL holder in Alabama.
Maybe this helps you some.???
I dont think a Florida FFl dealer would care what state you live in as long as you do not tell him your going to take the gun back to New York.
Easy enough to call a FFL dealer in Florida and ask or maybe one is on the forum.