Actually, transmission failure would not be covered as a collision loss because it does not meet the requirements for such coverage. Collision insurance is damage done your motor vehicle from striking someone or something so that path would be futile. What would be needed is some type of mechanical equipment coverage which unfortunately many companies do not offer, especially rental car companies. However, you could inquire with your credit card company just to see what they would say. That wouldn't cost anything to at least try.

Also, I don't see how a failed transmission is your responsibility regardless. Did you do something to harm the transmission (i.e. burn out the clutch, etc.)? It may not get you anywhere, but you may want to bring this up to the local authorities on St. Maarten to see if they have a position on tourists getting robbed like this. Just a thought.