I think you're onto something with your splitting of the NT into the earlier Jewish (Mark, Matt), and later Pauline (pretty much everything else - but including Luke) parts.
The Christianity of today is really much more the religion of Paul than of Jesus. That battle was won when the Ebionites and Gnostics were put down as heretics in Constantine's day (once the religion became an instrument of state power). It's very hard to know what Jesus was really about - so thorough was the Pauline victory. Naturally, all non-approved religious texts were burned.
However, in recent decades, some ancient (and hence uncensored) texts have come to light (see Lost Christianities). It seems clear enough that:
1) The original followers of Jesus were Jews.
2) The original Jewish followers of Jesus became the Ebionites.
3) The Ebionites had a single gospel - Matthew, minus the virgin birth.
4) The Ebionites believed in one god (like the Jews) - not the Pauline trinity.
5) The Ebionites kept Jewish law.
6) The Ebionites considered Paul to be a heretic.
Paul's religion started within a few years of Jesus's death. Paul was very big into prosyletizing - hence, his religion spread. Luke was apparently Paul's secretary/doctor/accolyte. In general, Pauline theology is much more elaborate than Ebionite theology - if you compare Luke to Matt or Mark, you see this elaboration. John came much later, and seems to be utterly unconnected to anything Jewish - it's purely Pauline.
So, the Ebionites held sway in the more traditionally-Jewish areas (Middle East), while Pauline ("proto-Orthodox") Christianity spread thru the rest of the Roman world. In particular, it became dominant in Rome.
None of this would have mattered, except that Constantine (300 years later), out of the blue, decided to make Christianity (very much a minority religion at the time) into the state religion of the Roman Empire. Which variant did he choose? Naturally, the Pauline variety. At this point, all competing Christianities became illegal - Ebionities, Gnostics, etc, were branded heretics, were executed (if they wouldn't recant), had their texts burned, etc.
What I'm getting at is, if you're going to call Pauline theology into question, you've got a whole lot of unwinding to do! There's very little left of non-Pauline Christianity to fall back on. You'll have to go back to the most ancient, pre-Pauline texts. Then, you'll need to start keeping Jewish law, stop believing in the divinity of Jesus, etc.