As noted, this would be a violation of the Passenger Vessel Services Act.
A foreign flagged ship cannot transport passengers from one US port to a different US port without a stop in a distant foreign port. A distant foreign port is any port that's NOT in North America, Central America, the Bermuda Islands, or the West Indies (including the Bahama Islands, but not including the Leeward Islands of the Netherlands Antilles, i.e., Aruba, Bonaire, and Curacao).
It matters not that it's two different cruises that you're proposing to take, it matters (to the law) where you get on and where you get off the same ship. In your case, you're embarking in NY and debarking in Miami.