Some premises that may be faulty
1 - that the death penalty is contradictory to American values
This is just BS. Some people claim that life has inherent values. But you see this nowhere in the documents from the time of the founding of the nation. What you do see is people trying to make something of their lives - trying to give their lives values. Eliminating a murderer is just like getting rid of the trash as far as society is concerned. I fail to see the "non sequitur" with regards to saying that since someone can't bring back a person they killed their life is forfeit. It follows one to the other - a life for a life. It's still not enough, but it's all we can do.
2 - It's impossible to ever be 100% sure about a murder conviction
Again this may be true most of the time, and if you wanted to argue that the death penalty should be rare, then I could accept that. But to eliminate it as a possible punishment completely is ridiculous. If any of these high school shooters had been caught in the act, then you would have had a 100% certainty of having the right person. multiple eyewitnesses, even video footage in some cases. It might not be possible to be 100% sure all the time, but in those cases where it is possible, the death penalty should be implemented speedily.
3 - primitive justice systems don't work/we've evolved past x system
Just looking at crime rates puts the lie to this one. In the end there are only 3 principles that one can look at when dealing with criminals: 1- rehabilitation 2- retribution 3-rectification
We've seen that rehabilitation doesn't work. I would argue that even if it did, it isn't the state's job to "convert" criminals to an honest life. Retribution is really only half justice, and it's true that there are times when that's all we can get, it certainly isn't perfect. This is really where the death penalty fits in. It is a commensurate punishment for an act that can't be redressed. Third we have rectification/redress this is true justice. The criminal gets nothing out of the crime and has to pay back the victim/society, and the victim regains what they lost. It is justice on both sides.
It is true that no system can rely solely on any one of these principles, but we can prioritize them. My own priorities would be 1- redress and 2- retribution. I would leave rehabilitation to the criminals themselves.