Is the death penalty unconstitutional?
...they totally botched their most recent execution: it took TWO doses -- and it took about 34 minutes for the person to die!... - which would make it unconstitutional, as "cruel and unusual punishment."
You mean are certain death penalties unconsitutional, those involving a particular method of chemical injection.
No ethical medical doctor can partake in an execution -- it goes completely against their Socratic Oath: do no harm.
That is not a constitutional issue.
The two parts are related: doctors are well qualified (medically) to properly administer the injection -- but they are barred from taking part by their oath to do no harm. The poor persons who's job it is to execute the person are not medically trained (in all cases, anyway), and they obviously, can make mistakes.
Also, the three drug cocktail that Florida uses, along with most other States that still execute people, is simply not always effective, and (apparently) it can be done incorrectly. And, it might be causing a lot of pain before killing the person.