Well, I don't mind taking a shot at this.
The biggest problem I see with your proposition is that you have to argue that James and Paul preached different Gospels. Since Paul claims that James approved his Gospel--yes, to the Gentiles, but not a different Gospel--and history says that the Jerusalem church and other churches remained in fellowship as followers of one Gospel, then I see a problem with the argument that James & Paul had a different Gospel.
In front of James, at a meeting that James seems to have been presiding over, Peter said, "Why tempt ye God, to put a yoke on the neck of the disciples, which neither our fathers nor we were able to bear?" Then he added, "But we believe that through the grace of the Lord Jesus Christ
we shall be saved, even as they" (Acts 15:10,11).
Just before that, he had said, "God made choice among us that the Gentiles by my mouth should hear the word of the gospel and believe" (Acts 15:7). Notice that he said "THE Gospel." To suggest that James had a different Gospel than Paul doesn't fit with history.
The reason that everyone does that is because they don't understand Paul's Gospel. We've had 2,000 years pass, so it's been handed to us so twisted and corrupted by Protestants, starting with Martin Luther, that it's completely unrecognizable.
You wrote that Paul's Gospel is "APART from works." You mention that the Gospel of the Kingdom is "justified by works and not by faith alone." It is true, those are both bible quotes, the former from Paul and the latter from James. On the surface, they do seem to be absolute contradictions.
But if they are, then why does Paul say we are judged by our works repeatedly (Rom 2:6 & 2 Cor 5:10, for example)? Why does Paul list only works as the reason we enter or are barred from the kingdom (1 Cor 6:9,10; Gal 5:19-21; Eph 5:5-8)? Why does he twice say that it is by continuing to do good that we will receive eternal life (Rom 2:7 & Gal 6:8,9)?
Paul put a subtle and helpful twist on the way the Gospel was presented. Entrance into Christ is apart from works. You, being a sinner by nature, will never be able to overcome your sin and be judged righteous by God. Therefore, there's another way. Enter by faith into Christ, and he will transform you.
Martin Luther added a subtle and harmful twist to the way that Gospel was presented. He said even the judgment is apart from works. Enter into Christ, and Christ won't necessarily deliver you from your sin and transform you into a righteous man who can be saved at the judgment. Instead, he will make it so that it doesn't matter if you are a righteous man at the judgment. Even the judgment will be apart from works!
But that isn't true. Paul says repeatedly that the judgment will be according to works. Nothing has changed about the judgment. What the Gospel offers is a free entrance into Christ, where the Spirit of God will utterly transform you into a righteous man who will pass the judgment rather than fail it.
Thus, Peter is willing to tell even the saints, "If you address as Father him who impartially judges according to each man's work, then conduct yourself throughout the time of your sojourning here in fear" (1 Pet 1:17).
The problem with the seeming contradiction between James and Paul is their use of the word justified. Paul says faith apart from works, but when he says justified he means entering into Christ and having your past sins forgiven. That is by faith apart from works. (You'll see he's talking about the same thing in Eph 2:8,9). He is not talking about going to heaven, and whenever he does talk about going to heaven, he says works.
James, on the other hand, is referring to the whole of our salvation when he says justified. Therefore, he says works and not faith only, because he's talking about the future and going to heaven, not just about having your past sins forgiven when you enter into Christ.
With that contradiction out of the way, there's no reason for the dividing up you do. And that's good, because you're dividing up people who said they weren't divided on the Gospel.
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