I think people could fall into a spectrum between the axiomatic views you present depending on what is considered a capital offense.
For example I might be in favor of capital punishment but only in cases of war crimes. In that case, for almost all intents and purposes I'm against death penalty since I only approve of it in extreme cases, versus someone that is in favor of death penalty for rapists (assuming there is no uncertainty like in your example), since I could indeed imagine a rape victim that would like to have the rapist dead.
So I agree that if you have an axiomatic view as you put it, the rest of the (non-axiomatic) factors will not be of relevance to you, but then the problem becomes defining on which side of the slide do you consider your view to be axiomatic.
My point is that this almost seems as a sort of "fractal" discussion in the sense that you can always think of yet another factor that would establish different positions for two people although they might seemingly have the "same" axiomatic view, and that makes it very hard to discuss this subject without polarizing people.
There are reasonable arguments you can make about the death penalty, like uncertainty or cost or efficacy as a deterrent. They may even convince some people.
But a lot of people have an axiomatic view of the death penalty.
I personally hold the belief that killing is bad, and should be avoided, with some complicated feels towards self defense.
I may make all of the arguments above trying to convince people to oppose the death penalty. Hell, I may consider lying about the statistics. But they won't change my mind. If it's more expensive to not execute people or less effective at deterring crime, I'll still oppose the death penalty.
Uncertainty is no different. There is always uncertainty of varying degrees. There will be cases where the convicted is almost certainly guilty. Imagine a suspect commits his capital crime in full few of a large crowd of unbiased witnesses, many of who knew him personally and can clearly identify him. Moreover, he was taken into custody immediately after committing the crime, by police officers who also witnessed the crime. He gave an unforced confession, gave details not available to anyone else, and offers no remorse. He is mentally competent by any measure.
Add in any other caveats you'd like. If you are still opposed to the death penalty in this particular case, well, then you're not really concerned about the uncertainty, you're just opposed to the death penalty. If you aren't opposed to the death penalty in this case, then isn't it really just a matter of improving our definitions of "reasonable doubt" for capital cases?