I thought more about that while writing this paper on the Falkland Islands. To be sure, the U.K. provides the justice system in the Islands because they are a British Overseas Territory. So, the circumstances are different from charter cities, but the case made me think that actually buying justice from another government might work.
An excerpt from the case:
It is likely that by per-capita standards the Falkland Islands will become one of the richest societies in the world. According to some assumptions of oil prices and population growth in the peak years of oil production the GDP of the islands could reach between 675 and 1,000 million, that is between US$189,000 and 280,000 per person per year.