It shouldn't take 4 months to get your passport. When I did mine a few years back, it was much faster than they said to plan for, something around 4-5 weeks. If you still have 4 months between now and your trip, there's no need to pay for the rush. It will be done well before then.
Not sure how long you have in Belize, but be sure to do some kind of excursion, whether through the cruise operator or on your own. Belize is an AMAZING country, and Belize City is not at all representative of what Belize has to offer. If you spend your time in Belize City, you'll be sorely disappointed. If you're not a diver, I'd recommend the Caves Branch tubing trip - floating down the Caves Branch river on an inner tube through a series of caves in the rainforest. AWESOME.