Is Romans 7 about life as a Christian?

I was involved in a Calvinist/Reformed discussion on Romans 7, specifically discussing whether Paul in Romans 7 is speaking of himself as a "Christian struggling with sin" versus whether Paul here is speaking of his former life as an  "unconverted Jew". Biblical commentators have argued both as possible readings, but generally the Protestant side (especially Reformed and Lutheran) comes down strongly on the "Christian struggling with sin" reading of Romans 7. While that Protestant reading is understandable, I think it is a very problematic and inferior to the more likely "unconverted Jew" interpretation of Romans 7. This might not seem like an important debate, but I think we really need to care what Paul actually wants to teach us in Romans, and we should care if certain agendas are causing us to read Paul incorrectly in order to prop up erroneous theological ideas.  

Before delving into the text, it is important to affirm that everyone agrees that the Christian life involves an inner battle with one's flesh, which Paul speaks of elsewhere (e.g. Romans 6; Galatians 5:16-24). After we delve into the actual text and do actual exegesis, I will then share why I suspect the Reformed/Lutherans are trying so hard to hold to their reading.