There's more history, and less science, to Jay Chapman's invention of the three-drug cocktail than described in David Kroll's (great) article. Check out this amicus brief from the Berkeley Law death penalty clinic (PDF link, scroll down past the news articles -- page 17 of the amicus brief starts the really relevant bit) and Chapman's own words in an interview with Human Rights Watch.
Briefly, a couple of OK state legislators wanted to come up with a different execution method because it would cost too much to repair the electric chair. They asked Chapman, who was the state medical examiner, if he had any suggestions. Though he was not an expert in anesthesiology, pharmacology, or toxicology (and told the legislators as much at the time), he came up with the three-drug cocktail pretty much off the top of his head. It was quickly adopted into OK state law with little further research (they asked one other guy over the phone, two days before the law passed). Then a bunch of other states just wholesale adopted the OK lethal injection law, with no further questioning or research.
When asked by Human Rights Watch why he chose the drug cocktail he did, Chapman stated
“I didn’t do any research. I just knew from having been placed under anesthesia myself, what we needed. I wanted to have at least two drugs in doses that would each kill the prisoner, to make sure if one didn’t kill him, the other would.”
When asked why he chose to add potassium chloride to the cocktail, he stated
“I didn’t do any research … it’s just common knowledge. Doctors know potassium chloride is lethal. Why does it matter why I chose it?"
I'm pretty sure there is more research and regulation on how we put animals to sleep than on how we put people to sleep. I'm also pretty sure David Kroll, for example, is significantly more qualified to come up with a lethal injection protocol than the guy who came up with the one we use now.