Question: Do veterinarians have any trouble getting drugs to euthanize sickly dying animals?
Question: Do drugs in question 1 have any trouble working on humans, albeit, with appropriate dosages?
The purpose of judicial execution is to make a live criminal dead. For a variety of reasons, this process must be quick and free of sadism (I get the "do what he did to his victim" thing, I really do, but that will never be the law in a nation with an Eighth Amendment).
Hanging, beheading, and firing squad all manage the job reasonably well.
A century of "scientific execution" (gas, electric chair, lethal injection) has failed to improve the process.
To answer your specific question, who do you want to do the research necessary to get an answer and who are the experimental subjects?
IV techs, pharmacists, nurses and doctors have, and should have, a very high barrier against deploying their particular skill sets for killing people.
I'm very pro-death penalty, I think it's moral and just, but I would never, ever use any skills I've acquired in medical training to kill somebody. Pull the trigger, open the trap door, swing the axe - sure.
It's not surprising to me that medical staff at prisons aren't very good at this.
I favor a return to fast. mechanical executions (rope, axe, bullet), and if the people in their wisdom are too squeamish to allow it, I'd abolish the penalty.
Medical executions are exquisitely cruel, because they transform a caring act into a killing. They should be abolished.