1. Anarchy does not preclude a large degree of voluntary cooperation. What secures a voluntary society from being taken over by neighboring societies is free men agreeing to defend their society and making it too much trouble for any neighboring society to make the attempt.
This does require those participating to be responsible and bear the burden of self defense both individually and collectively, but I see no reason that such a voluntary alliance couldn't stand up against a slave army.
2. Problems? The first, I think, is simply finding enough like-minded mature people to get along and do what is necessary to create the society.
We need to figure out what needs to be voluntarily agreed on and then find people who have come to the same point where they voluntarily agree on those things.
You need enough (doctors and farmers primarily) to create a voluntary society in isolation---under the radar. The biggest initial problem is internal. Might be insurmountable---depends on personnel. But you have to have a critical mass of people who can create an independent economy and have enough agreement to get along. You have to determine the fundamental things people have to agree on, and what to do with people who change their minds later. But it's clear that internal conflict is the biggest problem/obstacle.
The second you've already mentioned. Self defense. There are two obvious strategies to mitigate against this problem in the short term. They are related. The first is simply to not be noticed. Drop out of the system and create an independent economy which is adequate in size for survival and defense but does not draw attention. Those who tend to come under fire are those who make waves or are already targets---open tax protesters, people trying to make waves in the courts, driving without licenses, etc. You've got to avoid those things which make a target of yourself.
Look at Schaeffer Cox. He was amazing. He had brilliant ideas. But he went around with a cell phone camera irritating the psychopaths, and they put him in a cage, and then they broke his mind. You can't do that. Instead you need to have control of the local police, and then you either convert them or become them. (And by that, of course, I mean you take over local policing with a voluntarist system---whether you want to call it "policing" at that point is irrelevant.
The second is to keep the level of known/publicized resources desired by the neighboring society to a minimum. You want to have a productive society, but it's not clear that you want it to be too openly productive lest you draw attention.
3. Not only is there a better way, I think that what you suggest (as a first step) is not a viable way at all. You have to take over a county. That is the first step, and given the prerequisite of mature people who can get along, it is *not* very hard. Attract others and take over several counties. One would need enormous portions of more than half the states under control before even thinking about abolishing the federal government. They will wipe us out otherwise.
Also, the colonists tried this against the British tyranny, and within a decade they had the same tyranny imposed on them again. If you're going to fight a war, you need to make sure you can win it and come out with something on the other side. It's not clear that anyone has been able to do that yet. We're certainly not in a position to do it.
We currently have enough freedom to do these things I've suggested here and now, we simply lack the courage and personnel.
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