1. Taxes:
So you incorporate on the BVIs or a similar tax heaven, because you don't want to pay taxes. You are not even using the infrastructure of a country, so that doesn't even feel morally wrong. But crucial parts of your company lay within the USA (servers, some investors, consultants, bank accounts..). There have been tax cases before (at least in Europe) where it has been argued that a server equals a permanent business establishment and therefore is taxable (I can not find an English language article on the quick but I remember a case where a german hat incorporated in Cyprus and used german servers). So that would be a mess.
2. Bank accounts
Does the country of the boats registration or the country you choose to incorporate have a stable banking system and currency? Can you get a Paypal (or whatever payment provider) account for this bank account? Or will you go for a US bank, which again leads us to (1), also I dont know how hard it is to open a bank account in the US on the name of a foreign company with no entity in the US. What will potential costumers think about bank accounts in county x? What happens if the US tightens rules on money laundry, making your transfers a pain?
Many questions will have to be solved on the way. I really hope the project succeeds, especially if it pushes US law-makers to think about their visas.