No need to use a South American insurance insurer, your broker might have not experience with international ops insurance and he's misguiding you (most likely unwillingly) or simply can't inure you within their scope of business.
Call this company: Wings Insurance
They have insured "N" registered airplanes for us with worldwide coverage, they might help you.
You don't need insurance for every country you plan to fly around central/south america and the Caribbean, a comprehensive regional coverage is sufficient. The only country that i know that uses an additional policy to fly within the country is Mexico, and that one is an easy one to obtain.
Hope it helps.