Disappointed about the Andeans and James's, but at least there's a definitive answer for once.
I just looked through my AZA spreadsheet and 26 include Caribbean on their websites vs 14 saying they have American. I prefer Caribbean for the same reason Jana stated. Thanks for the opinions. I'm relatively new to paying attention to birds, so I wasn't sure if it was like puma/mountain lion/cougar, where they all seem to be equally acceptable and used, or more like Siberian/Amur tiger, where one is considered correct and the other is outdated but still used.
Interesting about the Chileans, as well! Now that you mention it, the places I've been recently did seem to mostly have Chileans in older parts of the establishments, often large ponds with some other waterfowl near entrances or eating areas, while other species tended to be in newer exhibit areas and/or were much smaller flocks.