Each of these had a slightly different telling of what they thought Christ's nature was. And Arabia had the heresies that had been proven wrong elsewhere, like the Gnostics, Arians, etc.
Remember also that Medinah was a Jewish city and Mo took a lot of the beliefs of the Jews and twisted them (like having Abraham sacrifice Ishmael instead of Isiah etc) and Mo himself was illiterate, hence his retelling of the nativity in the Koran reads like the birth described in Revelation.
Finally, as you correctly point out, the concept of Jesus being a phantom also slips in and is also contradictory with another part of the Koran/hadiths that states that Christ was "replaced" on the cross and laughed at those trying to kill him..
After reading Hilaire Belloc’s chapter on Islam in the Great Heresies, it seemed as though he considered Muhammad to be a heresiarch who created a new religion on his own off the top of his head, borrowing from Christianity and Judaism.
To me, it seems like Islam was Satan’s response to Christianity, established through Muhammad, with the “angel” Muhammad was meeting in the cave being Lucifer. Is this view of Islam at least consistent with Catholic or historical Christian thought?