Salam Daniel
You wrote:
".... And yes, I believe the heritage of Christian and Jewish sources were vitally important for Muhammad. In fact this is central to the Islamic faith, the pillars of faith are Hebrew! Muhammad valued this, and corrected the Christians when they departed from its origins..."
We don't find any term by "Pillars of faith" in the Quran and you are probably referring to a hadith. Quran, being continuation of Allah sending revelations to mankind covers a lot of common ground between Muslims, Jews and Christians. It makes it a point to point to correct a few aberrations that crept in over time in what the people of the book believed. Muhammad was, as Allah's Nabi representing what was revealed to him and not "making corrections" on his own initiative.
Any version of history that we read pertaining to the life and times of Muhammad can be checked against the Quran, The Criterion.
Thanks anyways!