I like this but it is based on the assumption that all of the parties are rational. Unfortunately, The original question was framed "In the real world" where there is abundant evidence that ones foe cannot always be relied upon to be rational.

My favorite approach would be to stay hidden...as in the book. Better they not know about you.

"If so how would it be funded and managed?"
Ideally it would primarily be citizens, mostly with their own weapons and tools, organized into a militia force. Its goal would not be to stop an invading army but just to make it costly to invade. If they were guarding billions of dollars of precious metals, they wouldn't stand a chance. But they're guarding a small area with labs developing new materials, micro robots, software tools, ways to cram more data into a given about of spectrum, tools for analyzing DNA and proteins--- all the things investors around the world want to take a risk on to earn money. The value is in the international teams, the networks of angel investors, the conditions of motivated people seeking to live deliberately. The labs are owned by international investors and they partly colleaterlize debt instruments. Stealing them would be stealing from investors around the world. And once you steal it, you've destroyed the conditions where those international teams of workers are going to this remote place in search of freedom and wealth. On top of all this, many of the citizens are armed and organized into minutemen militia. Sure a really army would overrun the militia, but the army would also destroy the spoils they seek to plunder.

The point I was trying to make is "Would a "Gulch" need the equivalent of a military to provide protection against a hostile invasion force?" If so how would it be funded and managed? The notion that the Gulch could peacefully co exist in a world dominated by collectivists strikes me as naive at best.

An alliance with a nuclear power?

I think a liberty-oriented free zone would not be directly attacked. The value would be in their inventions, not tangible items that could be stolen directly. A militia of free zone citizens could defend against direct attack from extremists or nation states intent on attacking and keeping the spoils intact for plundering. They would not be able to plunder, so they would not attack directly.

The nation states of the world would “attack” the zone by not recognizing its sovereignty and not allowing their citizens to renounce citizenship and tax obligations. Free zone citizens who failed to pay taxes to their nation of origin would find their investments outside the zone frozen. Inability to for free zone citizens to make foreign investments or accept foreign investment would be a huge detriment.

The nation states would justify this by saying the zone siphons off the top producers, leaving the old nation states to handle the troublemakers and social problems. The free zone would respond that after a few generations, it has its own natural born citizens who are troubled, and the zone doesn't expect the old states to deal with them.

I'm not sure there's a solution with taxes and rules strong enough to placate the old states but not so high as defeat the entire purpose. It would involve citizens of the zone paying taxes to their states of origin, taking steps not to become a money-laundering contraband-trafficking haven, and having some sort of provision that future generations would not have tax obligations to the old states. It would be a hodgepodge of compromises with the old states, trade and the multinational companies that want to trade with the zone.

In the best case scenario, the world eventually recognizes them. A century later becomes a place known to foreign travelers as a “wild west” place for people looking for a new life and to make a fortune, a place to indulge vices of sex, drugs, and gambling, a place to see the iconic Dollar Sign monument visible from the port, and people with a distinctive sing-song accent that sounds Indian English but a few Chinese and Russian words thrown in. The key is for those people a century later not to become complacent when all those struggles get compressed in things get compressed into the Zurich Compromise, Washington Accords, and things for kids to memorize.

More likely scenarios involve it being brought back into an existing nation state and everything that goes along with that. I hope enough people try it that someone beats the odds and pulls it off.

Watch out for those individuals who try to fake reality. Watch out for PC and identity politics. Don’t allow these to take root in the society.
This done by well educated individuals not government force, unless crime(s) have been committed and then only the individual(s) properly tried and convicted are punished.