Let me present these tweets from Seth M. Ehorn for your consideration:
When we study the use of the OT in the NT should we consider the context of the composition of the OT passage to matter all that much since the Septuagint (or, Greek Old Testament) is used a majority of the time. For example, when Paul cites Habakkuk 2:4 in Romans 1:16-17 does the Hebrew text of Habakkuk mean all that much to Paul’s argument? Does the context of the composition of Hebrew Habakkuk influence Paul at all? Or should exegetes recognize that authors like Paul are engaging the Septuagint with little thought being given to the Hebrew text?
the archives near Emmaus 
Questions! In the Eastern church bibles, are the NT LXX quotations identical to one of the various LXX translations? If so, which one? I believe Jesus’ quotations of the Hebrew scripture were in His own language — which I believe to have been Hebrew not Aramaic — and the later authors/redactors of the NT Septuagintized them. Is there any evidence supporting or refuting this? Was the LXX ever influenced by other Greek OT translations or vice versa? What is the relationship of the LXX to the Peshitta? What are the OT quotes in the Shem Tov/Munster/duTillet Matthews based upon? What are the OT quotes in the various Hebrew translations of the Gospels/NTs of the 17th-18th-19th centuries based upon?
Brian–these are great questions, as always. But in Romans 1, I wonder if neither the Hebrew text *nor* the LXX meant all that much to Paul, since each has a pronoun (using Rahlfs text here) and he bypasses a pronoun in his quotation all together.
True, it is not word for word. I don’t mean to suggest that apostolic exegesis is reliant upon a standardized Greek Old Testament, just pondering aloud whether the Greek Old Testament, even in flux during the time of the apostles, might stand as the grounds for Christian theology from the beginning.
I don’t think the issue is whether or not apostolic exegesis relies upon the form of the Greek Old Testament that began to stabilize later as much as I am wondering out loud whether the Greek Old Testament is the Scripture used by the Spirit to guide early Christian theology.
Sure–definitely does seem to be that way!
Some good thoughts here in the post and in the comments (and thanks to Brian for the mention). To follow up from my own Tweets, I would qualify by saying, the Hebrew Bible would be important for Paul’s exegesis (in any given instance) if it could be proven that Paul cited from or knew the Hebrew Bible (in any given instance). The evidence, in my view, is overwhelmingly in favour of Paul citing from the Greek Bible. This should have significance for exegesis.
In the comments: Paul’s wording in Rom 1 is probably his own adaptation (see Stanley, Paul and Scripture; Koch, Die Schrift). Koch argues that the inclusion of the pronoun (in either of its locations in the LXX versions of Hab) would not cohere with Paul’s argument in Romans and that, therefore, it is likely his own omission. Paul plays by the ‘rules of the game’ (to borrow a phrase from Juel) when it comes to his perspective and practices on literary borrowing. That is, his adaption of this text (or any text, for that matter) is completely normal by ancient standards. In that regard, speaking of a non-regard or even a misquotation when referring to Pauline citations is, in my view, anachronistic. Cheers. -SME