Why can't we just put a wall around the state of New Jersey and throw the convicts in there? Technically a prison, but we don't need to pay all the upkeep of a prison, beyond making sure the wall isn't breached. The land is decent enough that they can grow food. Its not killing, and it removes them from society. And it fixes the problem of New Jersey existing. That shithole is an embarrassment and should be put to better use.

My point is, all the reasons for killing are moot while there are other options. 

The reasons you mention for killing sometimes being justified are really only two scenarios. Self defense and rebellion against oppression. And this is why IMO we should stop violating the 2nd Amendment. Those two scenarios don't carry over to the justice system. Justice is only administered with the defendant in custody, which means they don't pose a threat. The threat is neutralized. Justice can't be revenge. 

 I'd add a third scenario, vengeance.

You're talking about exile now, which I also think is justified. But now you've got to consider, is it just to put someone in a cage with monsters? If it's not just to kill someone for being bad to those around them, it's certainly not just to lock them in a cage with people who will prey on them, that's more akin to torture.

If someone is damaged in some way to the point where they present mortal danger to those around them, it is unjust to subject anyone to that behavior, even another like them.

I have some very unpopular views on this topic, and some popular ones, but I've thought a lot about it and I think I understand pretty clearly what a just justice system would look like, and it doesn't preclude the death penalty, or other corporal punishment, but it does preclude prison. 

 Exile, imprisonment, forced servitude as a monk while getting to know God... Doesn't matter. Imagine whatever. The only bottom line is that murder is wrong, for several reasons - its so wrong that its wrong from multiple viewpoints. Don't do it. The state is definitely committing murder when it executes someone because that person is already in custody. Not a threat. They are under control. So a jury deciding to kill them is no different than you colluding with your buddy to kidnap someone and then murder them. Its the exact same scenario. You and your bud may think you're entirely justified. Its the same.  

 Well, I think imprisonment is cruel and unjust, but aside that, you and I have already agreed that killing someone in self defense is just, and you haven't actually responded to my reasoning at all. You're reiterating your position, which is fine but doesn't lend itself well to fruitful discussion.

A jury, the state, all that I can agree with. That doesn't mean though that a group putting someone to death is always unjust, just that our mechanisms for doing it are.

I'd argue that me and my buddy deciding to go grab someone and kill them for, say for example, killing my cousin or raping my nephew or threatening to do so is entirely just. 

 Which part haven't I responded to? I'll do my best. 

 Well, youre saying "bottom line murder is wrong", I'm saying it's not always murder, we seem to be in agreement on that. You're saying when the state does it they commit injustice because of the process by which they do it, I'm in agreement with you. But you keep making those same points which aren't in contention at all and which we have already addressed. 

 I think I used up all my brain cells this morning. Anyways... I can respect that you read everything and still disagree.  

 A jury is explicitly not the state. 

We haven’t had real juries for a long time. 

My entire argument about death sentence rests on first restoring the true jury trial. 

https://mises.org/library/book/lets-abolish-government