Alternatively, just don't execute people.
It's always the weirdest thing that anti-government folks also have a pretty strong tendency to trust the government to perform executions. It's, like, I know what's actually going on there, but it's still frikkin' weird. Someone won't trust 'em to collect or spend taxes or regulate pollution or something but
will trust them with the authority to kill people. Makes no damn sense.
But yeah, just don't execute people sounds like a good baseline. Real hard to fuck up killing the wrong person or in the wrong way if you're just not killing people. Easy solution to stop issues related to the practice from happening, don't do the thing to begin with.
Nitrogen Hypoxia is probably* painless, it just takes a while after you fall unconscious to actually die.
It is (inert gas asphyxiation is one of the best methods of euthanasia we're aware of, so far as distress is concerned, and nitrogen is a primary vector for it), but the question I'd have is if that's what was actually
used. It's frikkin' alabama, odds they screwed up whatever mixture was involved ain't low, and from what I recall a lot of providers of material for that sort of thing refuse to provide for purposes of execution. It's entirely too possible they just botched shit.