I would fedex the box to Hyde Shipping in Miami.http://www.hydeshipping.com/3/default.asp?p=home
Hyde would charge around $65 to ship it to Belize City. You'll have to clear it through customs once it arrives. Sometimes you can clear it by yourself if you have receipts, if not you'll have to get a broker to clear it for you.
You can call Hyde and see what time their vessel leaves for Belize City, takes about 3 days to get there roughly. The boat leaves around twice a month. I havent used Hyde in 5 years, so their prices and departure times may have changed.