Check out the web site for Brian Harris at Seahorse Diving. (http://www.belizescuba.com
Brian is the best at finding the whale sharks. The best time is usually the two or three days after the full moon in April ,May and June. It is a full day trip. You will get back after dark so it will require you spending the night in Placentia.
Sounds like you may be trying to do too much in the time you have available. Better to plan another visit when you can. Enjoy the country and get to know the people.