Was the Rumbling in Attack on Titan ethically justified?

My understanding (correct me if I'm wrong) is that, when he made contact with Historia's hand, Eren saw all possible futures and concluded there was no other way to successfully avert the extermination of his own people.

He saw the one future, not other futures. And because it was in line with what he wanted it didn't change.

A "partial rumbling", likewise, would forever harden the resolve of the survivors to find a way to eliminate the Eldian threat.

I mean him destroying 80% of the island did just that and it was destroyed later. He foresaw that he would only destroy 80%, so doesn't that just mean his plan has the same problem? He's also got god-like powers and can destroy every military base and control a good chunk of people on the planet. Worst case scenario, he can just take over the world and create a benevolent dictatorship, then reeducate people to not be racist. That's not in line with his view of "freedom," but if his view of freedom says killing 80% of humanity is better than a temporary benevolent dictatorship he can control, I don't think it's ethical.

A reasonable understand of self-defense is not utility-based. It is within your rights to fatally shoot ten strangers in order to defend yourself from being murdered if escaping or negotiating your way out of danger isn't a viable option.

Self-defense gives you right to kill ten strangers who are trying to kill you but not ten innocent strangers. Attacking someone is assuming responsibility for the consequences of that, but innocent people are not assuming similar responsibility. So killing the attackers is not a violation of rights since they have forfeited their rights, but killing innocent people is.

Self-defense is a prima facie right that same way every right is a prima facie right. Do I have the right to go to the bathoom? Yes. Do I have the right to kill innocent people to get to the bathroom? No. Do I have the right to get a job? Yes. Do I have the right to kill innocent people to get a job? No. etc. Self-defense is a prima facie right because when we talk about "self-defense" we typically mean actions that don't violate the rights of others, just like everything that doesn't violate the rights of others is a prima facie right. Eating food is a right cause it doesn't violate the rights of others, but if it does (like cannibalism or something) then it's no longer a right.

We could say utility is not a justification and individual rights are paramount, but a deontologist view seems much more likely to be harsh on Eren since it would say the ends of saving oneself do not justify the means of killing innocent people. See pacifism, which is very deontological.

In real life, few people would choose to let the entire world lynch them if they had a magic button that could kill all humans besides themselves.

Eren's plan did involve him dying and led to some of his friends dying (Sasha, Hange), really he was mostly saving strangers cause he could have escaped with his friends anyway. But he killed more strangers than he saved. (And remember, the "entire world" that's attacking the island is most world governments but not every individual.)

I think only the rare person who, with sound knowledge of their own true character, can honestly say they'd choose to die has a right to say this is the wrong choice to make.

So just pretend that hypothetically, that perfect person exists and makes all the arguments I'm making. How do you engage with those arguments? Because if there's an objectively right answer, then it doesn't matter where the answer comes from. A good argument doesn't suddenly turn into a bad argument because a bad person is making it. A chemist could provide proof a mixture is poisonous and then drink it; they'll die and they're an idiot, but the proof is still valid. However, if you really don't want to engage with someone less than morally perfect making a hypothetical argument, then just imagine it's a hypothetical perfect person making the argument and respond how you would then.

What complicates this is that Eren was killing a lot of innocent people in order to achieve self-defense. So in order to protect himself from a country full of warmongers, he would basically wipe it off the map including the children there. Which, to be fair, was the most straightforward method of defense, since it wouldn't be easy to pick out just the guilty people. But it does make it more like a weird version of the trolley problem than straightforward self-defense.

If the only way of self-defense was to destroy both guilty and innocents in a specific group, then anyone who prefers own survival would just destroy them. Person who doesnt prefer own survival would just die instead.

Yeah but the question is, is that ethically justified?

Depends on what person considers to be ethically justified. Trolley problem becomes a lot different when you are the one who dies.

Incentives become different, but I don't think what is objectively right or wrong changes. In any case, the people evaluating the problem (us) aren't on the tracks, so it's not too different from standard trolley problems.