"Quit punishing businesses for hiring Americans and being based in America, and they won't put their headquarters in Bermuda."
Let them move off shore for tax reasons if they want. They shouldn't get gov't contracts if the do though.
The only thing that they have in Bermuda is a mail drop.
The company is otherwise in America.
But if I'm reading you correctly, they should be required, as a precondition of bidding on government contracts with their attendant paperwork, is to pay enough in taxes that they could very well lose money on the privilege.
As it is, most consulting firms call working for the government "pro bono work."