"then any argument that a life is inviolable goes out the window."
Very few people argue that. Even fewer people who are pro-capital-punishment would argue that, for obvious reasons. An argument that only convinces those who already agree isn't even an argument.
"An execution has all the hallmarks of something that would tick every possible mark of a particularly heinous murder otherwise."
No, it doesn't. You're just doubling down on the sophism. Again, let me emphasize that if anything, I'm angry that this is a bad argument against capital punishment, not as a defense of capital punishment. Everyone from philosophers to the man on the street have understood the differences between cold-blooded murder, murder in the heat of passion, execution, warfare, and self-defense for millennia. Nobody who is capable of making those distinctions is going to be convinced to see all killing as equal, when even the man on the street considers it a rather unsophisticated position.
See also why the animal rights argument that "if it's wrong to murder people for premeditated reasons it should be wrong to kill animals to eat them" hasn't gotten any significant traction. Appealing to people to deliberately dumb down their morality for that to work isn't a good argument, especially when, again, it's not even that sophisticated a difference we're talking about here. We're not into weird Latin terms, reading 19th century existential philosophy, or even arguing what "begging the question" technically means, we're talking stuff that your average 12 year old could explain.