The legal system is beyond reasonable doubt, which is why I deliberately said no doubt what so ever. To emphasise that I intended to specify a superior near absolute level of proof of guilt, which is possible for some types of crime.
Here's the problem with that view - you could end up with two dangerous situations.
1) If the death penalty is the only option for a murder conviction, juries could be less likely to return a guilty pledge (there shouldn't be any difference legally, as the jury still need only determine guilt beyond reasonable doubt, but I suspect that many jurors could be more wary of sending a person to the gallows, particularly since it will be expedited and irreversible).
2) If the jury have to determine whether or not the death penalty is to be employed (as is the case in the US), then you've potentially created a loophole in the system. Suppose the jury find the defendant guilty, but do not opt for the death penalty in a system where the death penalty is reserved for cases where we have no doubt whatsoever about their guilt (to use your words). The defendant who is not sentenced to death could quite easily appeal their whole conviction by claiming that the jury had sufficient doubt that they were not put to death, ergo the whole conviction could be quashed. I have no idea if that would hold up in an appeals court (as you have said, there is a difference between "no doubt" and "reasonable doubt"), but I don't really want to find out.
Life without parole is a preferable option when you look at the evidence, IMO. A miscarriage of justice can be reversed (you can't give that person back the time they've lost whilst in prison, but at least they'll still have a life to live). All murderers are tried to the same standard (guilt beyond reasonable doubt resulting in a custodial sentence). It's cheaper. There's no evidence that it's any less of a deterrent. It's less controversial and more publicly acceptable, and the ethical quandary is much less. One could even argue that spending the rest of your life in prison with no possibility of release is a harsher punishment than death.
And yes, you are correct that there is considerable uncertainty about what happened to him, quite a few historians think the traditional accounts of his gruesome death were just propaganda, and at least one researcher has