Four Twelve things seem to me to be crystal clear about the quest for the historical Muhammed:
Even before the beginning of the eighth century CE and--well, up to today--the example, words, deeds, and legacy of Muhammed have been mighty powers to conjure with throughout the whole of what was to become and is now Islam.
Thus every faction making a play for power and authority in the first century or two AH had to construct a direct, personal, recent, family link to Muhammed--the Party of the Family of Ummaya through Kalifa Uthman's marriage to Mohammed's daughter Ruqqaya; the Party of the Family of Abbas through Uncle Abbas, Muhammed's guardian after the death of his father; and the Party of the Family of Ali through Ali's status as favored cousin and son-in-law. Only the Party of the Purchasers of Eternal Life had no such connection--and they did not do so well…
There was, originally, a flourishing, reliable, and important set of traditions and beliefs about the life of Muhammed, and people cared deeply about Muhammed's words and deeds and legacies and example.
Hence every faction sought to find examples in Muhammed's life and words--or, rather, to forge examples--that would say that their view of the umma was Muhammed's and they were Muhammed's favorites.
Hence the real information about the life of Muhammed that was in the tradition has been drowned in a sea of forged ahadith, and what has authority now is what sounded good and was politically useful in the eight, ninth, and tenth centuries CE, rather than what was true of Muhammed's life.
Something very much like our Qur'an existed and was very much worth quoting before the end of the seventh century CE--we see it on the walls of the Dome of the Rock.
Before the end of the seventh century CE it was a winning political move to proclaim the shaheed prominently--as we see on the coins of the Kalifa Abd el-Malik and before him the Anti-Kalifa Ibn al-Zubayr.
From the death of Muhammed to the late seventh century, the Princes of the Arab Conquest found it wise to portray themselves as broad-church Abrahamic monotheists, as rulers who had inherited the God of Abraham through Hagar and Ishmael and would not persecute Jews or Nestorians or Copts or Nazoreans (or even the Khalkedonian Orthodox so long as they behaved themselves)--and to soft-pedal when talking to outsiders what Muhammed meant to them.
And Muhammed was, from the beginning of his preaching, in a very contentious dialogue with the Khalkedonian Orthodox, at least--for Jesus (Isa) and against the Christ (the Logos).
And the fact that Muhammed was so incredibly and publicly important to everyone at the end of the seventh century CE makes it overwhelmingly likely that his example, words, deeds, and legacy were equally and extraordinarily important to the conquering Emigrants in the early and middle of the seventh century CD.
The Quraysh, however, are not to be found where they should be in the non-Muslim historical record.
The absence of the Quraysh is damned odd--but lots about history is damned odd, and very thin webs of speculation built on the absence of evidence are as strong as their evidentiary foundation