Stupid question but since you haven't flown outside the lower 48 do you have an eAPIS account for US customs? This is now a requirement for Part 91 (since April) on departure and arrival.
Just to make things more difficult, 10 Caribbean countries joined forces and now require their own online version of APIS. Check these links for more info.
Caricom > HOME
Caribbean Community (CARICOM) APIS | NBAA - National Business Aviation Association
Otherwise get your overflights, put the permit # in you flight plan and you're off.
Where will you be leaving from and where will you be clearing customs?