A fourth alternative is to leave, and a fifth is to not start a company at all.
Now you understand why the USA deploys 3-4x the amount of VC capital compared to the EU. And prior to the current administration, entrepreneurs mostly wanted to get to the US.
As far as I understand, the US taxes its citizens whereever they live (the third alternative I mentioned).
Are you aware that the US charges an exit tax if you choose to renounce your citizenship? And if you do not renounce it, they will tax you no matter where you live in the world?