Leaving from Miami, you can do any of the Caribean itineraries. Except for the southern, that one leaves from San Jaun.
The cruise you mention on the Triumph is a good one. They also have the Eastern (St Thomas, St Marteen, San Jaun or Half Moon Cay) and the Western - Jamaica, Grand Caymen, Cozumel. Any of these are good cruises. But since you have done Mexico, maybe the eastern is better for you to get the Caribbean feel. The one you mention is just fine.
If you can deal with the heat, the Hurricanes are really not a big problem. Unless they interfere with your departure, the ships will change itineraries to avoid any storms. Just don't be disappointed if they do and it still is a fun cruise.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise, Magic 1/14
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013