The "theory of rewards" was quite popular in the Evangelical churches I associated with right after I was disfellowshipped (almost 18 years ago now). I personally never bought into it, cause it sounded as a cheap and shallow way to harmonize (from Paul's perspective, cf. 1 Corinthians 3) a number of very different outlooks, betraying the originality and completeness of each one.
My take is that there are a number of "ways to salvation" in the N.T. And a corresponding number of "salvations". Let's take as one example the Sermon on the Mount. It doesn't imply "faith", "ransom sacrifice", "resurrection" and the like. A change of outlook, attitude, behavior, makes all the difference: stop judging, and you won't be judged. This was not meant to be a gem on the Pauline crown of "salvation/justification by faith alone". It is a quite different "Gospel" which stands on its own. And the same could be said of many others.