You can only contract with an AAIC that is authorized by your flagging country. You found the big one in MARLINK, they are authorized for dozens of flag states. You could try MARSATCO, but they are only authorized for some of the offshoreregistration havens (Panama,...). So, what flag is your vessel? Without that information no one can make a recommendation.
St. Kitts and St. Vincent seem to be popular with some of the second-tier offshore AAICs, I only see Dominica with the big boys (MARLINK, Stratos, etc.) which I suspect will all have similar costs. Sorry, don't have any recommendations. Maybe someone else will have experience.