"Firstly, the quality of the historical evidence for Jesus is higher than for any other ancient figure. We have WAY more access to a variety of sources about his life than we do for, say, Julius Caesar. But there is absolutely no doubt about Caesar's existence."
Point of information. That is a complete nonsense. For Caesar we have coins, epigraphy, other people's writings, monuments, inscriptions, and of course his own writing [see The Gallic Wars].
Most scholars accept that such a person as Jesus of Nazareth did exist, given the socio-political situation in first century Judaea. However, there is no contemporary evidence to support his existence.
"It is just unsound to argue that the man is some kind of legend like King Arthur. No respectable historian argues that - whether they are believers or not. It puts you completely outside the mainstream academic history community to argue that way about Jesus - which is completely different from being a Christian, of course!"
You need to distinguish between the flesh and blood first century Jewish holy man and the figure presented in Pauline Christology. The two are completely separate.
The writers of the four gospels were not disciples the names are psuedonymous and were added later. The earliest gospel is that of Mark written around 70CE probably for a Roman christian community. There is no evidence that 'Q' exists it is a hypothetical document named from the German Quelle [source]. The earliest exact reference to the NT canon as it exists today is by Athanasius in his Festal Letter of 367CE.
Finally, I'd hardly call the discrepancies between the four gospel accounts "tiny". They contradict each other on some major points.