That doesn't answer my question. What is the standard of evidence that someone can't be re-educated?

I'm speaking basically in terms of when you've "won," since in for example an insurrectionary situation it's really more of a shifting practical question based on the situation at the moment. I nonetheless think talking about what a dictatorship of the proletariat should do is helpful as a baseline, even if you and I agree that in more desperate situations things like summary execution become an inevitable necessity sometimes. I think this in part because it gives us basically the only really constant bar to have for reference and can be useful for grounding how we're reasoning before applying more complicating variables to it in other circumstances.

It would have to involve the affected communities because an important part of justice is that the victims feel they were treated and interacted with satisfactorily.

We can say that an important part of justice is that democracy is upheld, including by following the protocols established by democratic mechanisms, but that's neither here nor there in a question of what we should be advocating for, i.e. where we are trying to bring consensus to.

In most case, victims don't want the perpetrators executed. It's usually their families and tertiary people who do. But they must be made to feel safe and whole again to where they would feel comfortable living alongside their former captors. If they don't, you invite vigilantism.

I don't really know how to say this more nicely than just speaking plainly, but what you are describing is not a problem with the treatment of the convict, but with the attitudes of these secondary and tertiary parties. A desire for punitive justice, for revenge, is inevitably some combination of sadism and maybe some other forms of counterproductive moralism. We need to start from a place of recognizing that it's a backward social attitude and not pre-emptively buckle to hypothetical threats of vigilantism as though they are just a force of nature, any more than we should buckle to threats of vigilantism over other cases of blatant injustice (as killing someone over such threats would be). The answer here isn't to design the system so that it is willing to kill in cold blood if 2 - 5 people want it to strongly enough, but to have a functional political education so that vigilantism over not killing people enough isn't a problem at a systemic level. This isn't some fanciful proposition either, since there are plenty of countries where the death penalty is abolished either completely or at least de facto, and generally that's not motivating vigilantism for them.

If it were realistically possible to keep every single Nazi in some form of confinement/education indefinitely, that's the most palatable moral action. I don't believe that would be the case in the immediate aftermath of most situations.

Sure, but that's overwhelmingly a logistical question, which is separate from the aforementioned moralistic distortions.

I also believe that there is room to say that some people do not deserve the chance of rehabilitation depending on the severity of their actions. To let them live would be to withhold doing what is right now for a benefit that may never come.

You are question-begging that executing them is inherently right. That is simply baseless.

Nothing the members of Unit 731 could do would make up for their actions, even if they spent their whole lives trying.

There is no such thing as redemption for any of us. The bad things we've done in the past remain no matter what we do, and some hypothetical account of net benefit or detriment when weighing past actions against the positive actions someone can take in the future is an excellent example of why this moralism makes the world worse:

If I spend ~70 years being a terrible human being, like a war criminal or something, and then I perhaps have 10 years left to do positive things, we can say that my existence in the most optimistic case is a net negative for society, sure, if that's a framing you want to talk about. However, killing me at ~70 doesn't undo the bad things I did, it does not reach into the past and make a single thing any less damaging, all you've succeeded in doing is preventing me from doing positive things in the future. In effect, you have made the net impact of my life worse than it otherwise would have been (again, if that's a framing you care about, which I don't).

This invites an obvious counter: "But that's the most optimistic case! You could very well just continue to be a scoundrel."

That's correct. Most people underestimate what you can achieve with rehabilitation, but it's still true. However, the thing to consider is that me being a scoundrel while stuck in a re-education camp doesn't hold a candle to me being a scoundrel in my hypothetical war criminal past. It's overall a basically negligible negative, a much lesser negative than the positive impact if I actually was able to contribute positively in a more optimistic case. The average of these scenarios is weighted very plainly toward living being positive even if you think the better outcomes are much less likely, and I consider the average to be a very important consideration because we aren't really considering an individual case, we are considering the aggregate impact of many thousands of cases.

As you allude to, even the "negative" case of the stubborn war criminal can be viewed as still being positive in many cases if they are doing penal labor in the meantime that economically offsets the costs of their captivity, which can be true when considering the captive population collectively.

There is only one real question in this situation, and that's what will produce the best outcome for the whole of society. We should not let punitive sentiment get in the way of benefiting people.

I am also posting from the state of Minnesota where my emotions are inflamed by the murder of my neighbors, so you can also attribute my bloodlust to be using past groups as a proxy for what I feel should be done here and now, before the 'peace' has been established.

I'm glad that you see it as bloodlust rather than just self-evident morality. It's understandable why you'd feel that way and I'm certainly not trying to attack you for that, even if I criticize some of your assertions that seem to be predicated upon it.

I don't really have any answer for what you should do over in Minnesota, because that's a very different kind of situation and, as I said before, what should be done depends on shifting logistical concerns more than anything else. I certainly won't cry for any members of ICE winding up lying in the bed they made, even if I would advocate against putting them there in a situation where we had more leeway to choose as we wanted (which is not the present situation).