[DavidWoof]

You're greatly overestimating how much an oral tradition leads to fixed wording. This is a pretty well-studied field at this point in time, and non-poetry oral traditions just don't generate the kind of long word-for-word identical passages that we see in Luke and Matthew.

There's a lot of debate over the synoptic problem in the academy, but almost nobody doubts that the solution involves a literary source instead of an oral one.