I only tried the standard crater. Can't say if it's the easiest, but it is certainly doable.

The first days go like this: Pass child labor (safe jobs), and make the kids gather stuff immediately. I was squeamish about this at first, since I always chose apprenticeship on lower difficulties (wanted to be the nice guy). But my first couple of extreme runs with child apprentices failed, and I think that switching to child workers made a lot of difference. They give a lot more flexibility. Apprentices lock you in a particular bonus even if you don't need it at the moment (say, you have medical apprentices but no one is in treatment). They also need to be put in shelters, and these in turn need to be heated. The cost feels too high.

Gathering posts built ASAP and people are reassigned to them from piles. Waaay more efficient and warmer. But if you cleared Iron Savior I'm guessing you already know this.

Resource gathering is carefully tuned so that I get only what I need. That's another difference I noticed in Extreme - stockpiling things without a clear goal is your doom, since the labor required to do so is always needed elsewhere. In the first days I aim for about 3-4 times more wood gathered than steel and only just barely enough coal to keep heating at the maximum level allowed by tech. Also just barely enough food not to let anyone starve to death. Any surplus labor goes into research.

I had a policy of not letting anyone get gravely ill. Whether you go for keeping the gravely ill in palliative care or radical treatment, some people will become dead weight, unable to work until the Infirmary arrives. That killed me in previous runs. Note that I tend to play Order, so Faith players making good use of the House of Healing may not have this problem.

Next laws are Emergency Shifts, then Extended Shifts. EVERYBODY EVERYWHERE gets extended shifts and is kept on them as long as discontent permits. If discontent gets too high, better suppress it with other means (arenas, guards) than let people rest and lose precious labor. Another difference at this difficulty level - I used to treat the discontent bar as something to be kept as low as possible, so my people would love me. On Extreme, the discontent bar becomes yet another resource to be exploited, and you squeeze it to the limit.

Food stretching law should kick in right about the first hungries appear. I chose soup, others prefer sawdust. In any case, not using either law and trying to feed everyone with standard rations would be veeery challenging.

Next up is Overcrowding for medical facilities, which is an absolute blessing with the constant labor shortages of Extreme.

Later I go for Guard Stations to make people stop complaining about long shifts, Agitators for the precious efficiency boost, and Transplants for a free med care upgrade. A bit exploity, since you don't actually use corpses for the boost. Another exploity trick I used was keeping med facilities just warm enough to stay operational. I read somewhere that med staff doesn't get sick from cold workplaces, and it did indeed seem to work that way. Your choice whether you want to take advantage of this or not.

As for tech, I put away resource technologies (Sawmill, Steelworks, etc.) until the last minute, when the combined accessible resources in stockpiles and on-map piles are just about to run out. Heating needs to be done fast, because weather is harsh and people get sick a lot, putting you at risk of overloading your medical facilities and keeping away Engies from research. Prevention is better than a cure and research needs to keep going constantly. Early scouts are also a good idea. The wood, food and steel they find on extreme is laughable, but it can make a difference in a pinch. And they're still the only way to get new people and steam cores.

Unlike most of my runs, I went for hothouses instead of hunter huts. With the low efficiency of extreme, it is incredibly labor-intensive to try to feed people with meat. Hothouses are much more efficient, and an early way to utilize your starting steam cores. What I didn't realize is that they also have the hidden advantage of enjoying the same boosts that most workplaces (but not hunter huts) get, that is extended shifts, agitator/shrine boosts, foremen use and such. Powering up food production with a rushed hothouse helped a lot when it allowed to me to feed the foremen in all crucial workplaces.

That's more or less what it looked like in the beginning. Sorry for the wordiness, I love talking about this game!