I would paint before you left. Cayman Is and Providencia will not be a good place for haul outs and Panama is very limited and very expensive. Mexico would be your best bet, then California. You do not mention stopping in Honduras or Guatemala, but you can haul out there for good prices if you go that route.
If you plan on staying in California, do not put on TBT paint and check for which paints they do allow now.
Mark