Further, as attested by the occurrence of a number of theory-non-conforming instances of ironic speech, most purely pragmatic views of conversational irony have a limited sphere of explanatory sway.
I understand this to mean, more-or-less: "Most purely pragmatic explanations of how irony is used in conversation have limited use. This is evident from the fact that a number of instances of ironic speech do not conform to theory."
What's not clear to me is how the "pragmatic views" relate to the "theory". For the logic to work, the two have to be referring to the same thing (otherwise the fact that instances of ironic speech don't conform to theory says nothing very much about pragmatic explanations). The problem is that "pragmatic" specifically refers to something that is not theoretical. So, for me it doesn't quite make sense.
Most theories have a limited sphere of explanatory sway because each has to face ironic sentences that they it cannot explain.
To me, this sentence is easier to understand, and if it gets the job done for you then I'd tend to prefer it. It also avoids the pragmatic/theory confusion that I suffered with the first version.