But the act of requiring the chemicals in the first place, as opposed to just hanging or shooting, echos the protection of the 8th (separate, relevant ammendment) anyway, what with cruel and unusual punishment not being allowed.

Not to dog pile, but I can't emphasize enough how misguided this point is. Long drop hanging, firing squad, decapitation, and a handful of other traditional execution methods are all virtually painless. The thing about lethal injection is that it deliberately suppresses evidence of the victim suffering by paralyzing them, so there is no sign of them suffering even if they feel like there whole body is aflame. Other methods are much more transparent in this respect (except electric chair, which has the opposite problem of drowning pain responses in noise).