Isla Mona--not unless somebody populated the island with invasive species. PR never had monkeys to my knowledge. They do have research rhesus macaques that were let loose there in the mid 1930s, I believe, hence the name Isla Mona. They are confined to that small island. There are a lot of wild goats there, btw. Maybe that is what the OP experienced in his plate of food- goat.
In PR, egg laying hens (gallinas) are prepared for meals after they stop producing eggs. They are a bit older and the meat is tougher, but more flavorful, and preferred for soup or fricassee by many. This is your most likely culprit. The other possibility is a guinea hen, which has similar characteristics (more gamey), but is more likely found in more rural parts.
Then, we are talking a different set of islands. Isla Mona is the namesake for the Mona Passage which is the straits that divide PR from DR. It is the WEST coast of PR. Mona island is located there.
The one you are talking about is off the coast of Humacao--east coast. It is a tourist trap now. Mona island remains deserted, I believe, and only serves as a place for a lighthouse managed by the Coast Guard. We used to go goat hunting there, allowed with bow and arrow only; required permission by the Coast Guard.
Difficult?? Not at all. But, during the 60'swhen I used to go there with my 2 brothers (one was a naval aviator, so he got easy pass from Coast Guard), the underbrush was thick, very thick. Shooting an arrow through it was the hard part. Having said that, I was a kid then, I only went along for the ride and to be with my two best friends; I wasn't doing the hunting. Was fun. My eldest brother (the aviator) got a goat every time. His friends were not so lucky; one put an arrow through his wrist, as it snapped on string release!! Bloody freaking mess.....