People are surprisingly able to work out their own agreements.
As for tyranny, humans will always wish to lord it over others, and they will always recognize the personal benefit in falling in with a warlord on the rise. Your proposal is to select a ruler, in hopes of avoiding a worse ruler, whom you call a "tyrant". The problem is that whatever ruler you pick will see the personal benefit in advancing his power, and will without fail work toward creating the very tyranny you fear. The United States government isn't yet a "tyranny", compared to others, but it's heading straight in that direction, and well on its way.
The only effective way to head off tyranny is for a critical mass of people to resolve never to yield to tyrants, and to be armed. They will resist the imposition of a warlord until the last man falls. But they will also resist what you call "organizing". Suppose someone comes along and says, "I'll work out your interpersonal agreements! It's like this: you tell me your problems, and I tell you my decision. Then, my decision is law!" He would be ignored. If he attempted to enforce his "rulings", his victim would kill him in self defense.
Which brings us back to my assertion that humans aren't ready. A critical mass must believe in freedom. Today, most people would pick a warlord, get behind him, and attack his rivals. Too many people are still slaves to their tribal instinct. That's why I can't make the leap today from minarchist to anarchist--even though I recognize that every minarchy will always evolve toward tyranny.
some group of people is very free (and a few people oppressed? not clear on your reason for "a large majority")
The ruling class is always free, in addition to having the license to oppress. A senator can do anything he wants with his property, and can also expect immunity from prosecution for victimless crimes. None of government's infringements affect him personally. Taxes? He's paying himself. Airport security? He can fly privately, or in military transport, if he wishes. Water conservation laws? The congress building has vacuum toilets that work on the first flush. Speeding? "Here's your license back--have a great day, Senator! Believe me, I'll recognize you on sight next time!"
Freedom for a few is no feat. Freedom for a vast majority would be a landmark achievement.
absolute freedom (that would technically include the freedom for you to steal my car without punishment)
No, that isn't what "freedom" means. It means that anything goes, as long as all interactions between more than one human are fully consensual for all parties. The only fixed rule of society is the golden rule.
Within that, consensual structures can be formed. I can hire you, if I agree to and you consent to work for me. I can fire you, if you don't fulfill the terms of your contract. I can start a club, as long as every member joins of his own free will. We can kick people out of our club, if they break the rules they agreed to when they joined. You can form a "Fight Club", in which every member consents to have the snot kicked out of him. You can even form a club that plays "paintball" using live ammo--as long as everyone consents to being shot at, and no third parties are exposed to danger.
But all of that's secondary; as long as the golden rule is followed, no explicit social ogranization needs to take place.
the strength of the US conservative movement since the 1980s, even despite its flaws
If you followed FReepers reaction to Katrina, you'd notice that these hard-core "conservatives" were extremely supportive of Bush promising more than $200 billion of our tax dollars to rebuild New Orleans. Bush is the biggest spender in the history of the solar system. I'm not so sure conservatives will stave off tyranny. If that's the plan, then I wish they'd stop using tyranny to fight tyranny.
I don't think it is a cinch to come to interpersonal agreements that do everything well, let alone perfectly.
Actually, it is. I leave you alone, and you leave me alone. See how simple it is? If you got something I want, and I got something you want, we'll trade. Voila! Free market. Civilization ensues.
The reason it doesn't work is that unevolved humans are uncomfortable when they don't know who's the chief of their tribe, and they don't really believe in the golden rule either. So when someone says, "I'm your chief!" they feel genuine relief. Then, when the chief says, "He's our enemy!" they willingly attack him. Other humans, afraid of this new warlord, will ask, "Where's OUR chief?" Government ensues.
Humans will be ready for civilization when they are truly shocked, horrified and amused by that latter scenario.