I myself am convinced in the existence of Mohammed. He was a caravan trader who traveling from was to Arabians the glorious center of religion and trade, to cities that made Mecca look like a bit of a hick town. In places like Jerusalem, Edessa and Babylon he doubtless experienced Christianity and Judaism but was never properly catechized; I suspect when visiting some point on his journey he had intimate contact with some Gnostic or Arian Christians and he probably dabled in the occult.
Except that, Mecca wasn;t a trading center. Modern archeology shows that Mecca wasn't any such a place. One point that is mentioned in the book. All of the Muhammadan mythology comes from two centuries later in the Arab Caliphate, centered in Persia and Iraq. None of it is contemporary, Muhammad didn;t preach Islam. He preached a heretical form of Christianity. The Arab Caliphate preached, and likely created, Islam.
I myself however am prepared to accept uncritically the history the Muslims give us of Mohammed
Except that 'history' comes 200 years after Muhammad supposedly existed, and the most "authentic" aspects of it are, admittedly, less than 1% of the entire tradition that proliferated at the time.
Anyway, the book looks fantastic from the look of the sources he used. That's the heart of the issue. When you want to know the credibility of a book on history, read the sources.
He also produced a documentary here: https://www.youtube.com/watch?v=Rg8n5oGYECE