This is interesting to consider: the JF model reads G and R as fundamentally concerned with the opposition between earning your salvation through works or receiving it by faith; Campbell’s PPME model suggests that we should read it instead as a debate between rival accounts of theological foundations: is Christ’s work sufficient for our access to God, or do we need a “Jesus + …” gospel?
The latter makes excellent sense in light of 1 C, while the first sits much more uncomfortably alongside it. Consider the treatment of works (and merit!) in 1 C 3:12-15, which follows directly upon a clear assertion of Christ as “foundation” (1 C 3:11)! And then consider Paul’s easy shift from merit questions to highlight the unconditionally graced character of Christian life (1 C 4:7). We see the same easygoing movement (in the opposite direction), from grace to works in G 5:6.
This suggests that Paul’s main concerns are not about “earning salvation” — he clearly expects the Christian life to be one of desperate, often mortal effort. Rather, Paul’s overriding concern in 1 Cor., and arguably in G and R, is regarding the status of humanity’s knowledge of God (in the fullest sense of the word): cf. his lengthy discussions of God’s and the world’s wisdom in 1 C 1-2, 3:18-20.