Although it doesn’t seem to particularly impede @swamidass’s argument, I think it’s only fair to point out that massive uncertainties may not be an accurate portrayal of the situation. As far as I know all the evidence from recorded history is on the side of the Gospel’s being written by whom they are attributed to.
The massive uncertainties, as far as I know, are basically arguments from silence, which, in the face of actual positive evidence to the contrary, are pretty feeble arguments at best. So maybe what may be a better portrayal would be massive arguments from silence, although I’m also not sure if there are that many of those to qualify as massive.
And regarding when, the only evidence I’m aware of for late dating is based on the assumption of naturalism. The argument goes something like this. Because of the prophecy by Jesus in Mark of the destruction of the Jewish temple which happened in A.D. 70, Mark had to be written after that, since prophecy is impossible. And since Mark was the first of the Gospels, all the rest had later dates. If you don’t assume naturalism that argument doesn’t fly.