The textual criticism of the Qu'ran was done by a German scholar just a few years ago and references to it can be certainly be found online. My source for the tradition among Arab Christians is Arab Christians -- I serve a little mission of the Antiochian Archdiocese as its council president and a subdeacon (in Greek usage a glorified altar boy with special duties at hierarchical liturgies, in Russian usage a very minor clergyman), and we sometimes have people from the Old Country (meaning Lebanon and Syria) visit. I've discussed the matter with them face-to-face. The coincidence of the name of the Assyrian bishop of Kirkuk with Mohammed's source is my own observation. I can't find where I learned the bishop's name, and my source may have misidentified him as the bishop of Kirkuk -- there was a Mar Gabriel of Kashkar, a city further south, contemporaneous with Mohammed's early preaching who founded monasteries in Mosul and evirons (see
here).