You're looking at 75 miles of travel, a lot of it in open deep water. If, and that's an unlikely if, you could find a boat big enough it would cost you a fortune in just fuel alone. Much cheaper and quicker to fly.
We have a party of 8 and with airfare and car fees, the total to transfer everyone will be close to $1000. It seems there are boat charters that do weekly tours off thr coast. Wouldn't it be a similar thing, but just for 1 day instead of a wewek?
You might contact Raggamuffin Tours and see whether they will charter a sailboat down to Dangriga. I know their 3 day sail down the coast stops at Tobacco Caye. Otherwise you could try the water taxi people for one of their smaller boats.
A San Pedro to Belize City charter (half that distance) is Bz$800 - 1000 and that is a local discounted rate when football teams etc travel for away games at cost. The fact you want it one way doesn't matter as it will have to return to it's start point. Raggamuffin might work on the way back from a trip but it's a sailboat and would likely need an overnight stop. Consider Express Bus to Belize City and water taxi from Belize City at around ~US$25 per person.
Just checked the Raggamuffin site and the Tobacco Caye charter is $275US per person. Phil's right, bus and water taxi are the cheapest. Flying from Dangriga to San Pedro would be a total cost of $612US.