It sounds like you have plenty of time, so the best option (if you choose to fly to Cancun) might be to get to Chetumal by express bus, and then get one of the water taxis from Chetumal to Ambergris.
The Mexican ADO express buses are excellent. There is an ADO Riviera airport shuttle bus from Cancun airport to Playa del Carmen -- stay there for a couple of nights if you wish, then express bus to Chetumal.
I have written more details about this trip on my BelizeBus site:http://belizebus.wordpress.com/
The site has links to the water taxi websites where you can see the schedules & fares.
Another option -- there are transfer services that can pick you up at the airport and take you to Chetumal or to Belize. See the BelizeBus site for links to some of them.
You might also want to research flights to Mexico City where you can get a flight to Chetumal.