I’ve found that conservatives are about 30-70 on the death penalty. I’m in the 30 and I agree with your reasons.
However, I think the death penalty needs to be retained, but only used on criminals that have BOTH:
(a) committed a henious crime, AND
(b) have proven themselves to be unincarcerable (through escape attempts, serious injury to inmates/guards, or are otherwise a military-type break-in threat - such as Saddam Hussein)
My position is a variation on yours: reserve death for somebody who has committed a capital crime AND has two or more violent felony convictions (for separate crimes, not multiple convictions for the same incident), for crimes where the victim would have been justified in using deadly force to defend himself from.
My reasoning is that the probability of a complete innocent getting three separate convictions is vanishingly small. Thus, even if he is executed and it's later found out that he didn't do the crime he was sentenced to death for, then I won't care.