The first question is not a question, it’s a demand: send us all your flight logs that you’re required to keep along with a business justification for each one, especially the flights to the Caribbean and Europe.

This seems pretty easy. If someone is going to the Caribbean all the time on a corporate jet, there should be business interests on that particular island. Unless their business is hospitality, they probably aren’t actually doing business on that island. So the use of the jet is taxable income.