If you own those properties free and clear or with substantial equity (as in you only owe 40% of the value) then you might be able to work a deal. I know lenders that do Foreign National deals but honestly I don't know what their cash out policies are. Otherwise you might have to go a Joint Venture or Equity Partner route. See if you can find an experienced mortgage broker in Florida that understands hard money, private money etc.
@Nat C. What you are looking for is a banker that can do mortgage loans for foreign nationals. I can do those.
PM me if you would like to explore options.