Your idea is sound but the next political division down is the state - not the city. You are 2 Civil Wars ahead of the curve.
I understand, but chartering a city does not result in a civil war. No state is going to secede, nor would the fed govt allow it (regardless of original terms of statehood).
People are far, far too timid to organize a secession movement. I’m trying to offer something realistic, though even a city would take a generation to beef itself up into a plausible contender.
And if it were mine to name, I’d call it Tax Haven rather than Liberty City. But I’m a cynic. :)