This is my interpretation of Space law based on conversations with people who have studied space law, law of the sea, property law, international law, and contract law in a number of countries and my own research.
The Outer Space Treaty is the main basis, and it requires a treaty state to be responsible for the actions of any non-government or other entity.
- The natural resources of space should benefit everyone.
- Anything constructed belongs to the constructor.
- The constructor is governed by the laws of their nation.
- As a USA Citizen you are free to give up your citizenship and thus your future rights and obligations to the USA.
So assuming you offered to compensate or benefit "Everyone" fair value for what you used and some rent for the space you occupied, and you did so compliant to USA law the answer is you could go to Mars, or anywhere else extra-planetary construct what ever was necessary to function as a productive USA citizen, pay taxes and expect reasonable support from the Federal Government. Eventually a sufficiently large number of people would be able to apply for state hood.
If you choose to exercise your right to terminate your citizenship, then you need to join another sovereign treaty nation or be recognized as a sovereign nation and sign the treaty.
To pay to "Everyone" you would probably be covered if you paid some "reasonable" amount into a trust used for general benefit.
I would suggest 10% of costs would be sufficient.
I am not a Judge (potentially able to set precedent) or even a lawyer.
I am involved in a project to simulate 1 billion plus people living in space.