My argument was not to demonstrate that any given execution method might be bad, but the context in which something occurs fundamentally changes the nature of it. Because this method of execution is used in other ways in completely different contexts it does not necessarily mean it would be less painful or traumatic than other methods.
The nitrogen chamber appears to be less violent than a firing squad, but it is not certain whether this is the case. The purpose of banning certain execution methods and allowing others is not that one is cruel and unusual and the other is less so, it is to obfuscate the brutality of what executing a person is. If firing squad was the only allowable form of execution more people would oppose it due to the very clear presentation of what it is regardless of that method potentially being far less distressing and painful than the use of a small gas chamber.