As a former juvenile hunter I know "the thrill of the kill" can be powerful and unthinking. Unless the island residents can somehow instill the inherent values of a diverse wildlife environment before the boys (mostly) enter that phase, this is likely to continue. I eventually came out of mine when I was caught then taught by a mentor to appreciate the beauty and value of wildlife simply for the sake of their existence and enrichment of ones environment. I would extend that concern to any of the islands reptiles including boas, which unfortunately, often seem to be the victims of simple fearful human reaction.
I should add that I'm not averse to hunting for food, but I'm reluctant to say make anyone apprehended eat their kill simply from the standpoint that iguanas are completely palatable when grilled over hardwood coals and sometimes referred to as "jungle chicken". You might not want to inadvertently trigger that as additional pressure given a declining population. But, given modern tastes, I rather doubt that as a likely scenario!
First step might be for Town Council to pass an ordinance protecting the Caye's reptiles..of course that does require a degree of enforcement to back it up...