Most Toyota vehicles built to be sold in the North American market (manufactured in the USA, Canada or imported from Japan) have been certified to run well (fuel savings with engine wear protection) on full synthetic 0W-20. This was mainly driven by fuel economy and emissions requirements. Other countries recommend the use of slightly heavier oils (5w-20 or 5w-30 are popular). What's not completely clear is whether there is any manufacturing differences (cylinder honing and treatment, for instance) between engines that are sold in different markets. I kind of doubt it, but one can never be 100% sure....
You have an interesting situation as your vehicle is being operated in the Caribbean. From the "B" pillar build plate, you can probably determine where your vehicle was built, and if it was certified for US/Canadian sale. It might have been imported to the islands from South America or even Europe. Was it sold to you and being serviced by a Toyota authorized dealer? And if so, which Toyota authority?
My thinking (totally non-scientific, just seat of the pants....): 10w-30 is pretty old school. Try 5w-20. Others in hot climates seem to gravitate towards this grade. Change it every 5k miles or less to be sure.