I agree with most of what you say, except that Paul did not author a Gospel. Matthew, Mark, Luke, John, and whatever you personally admit to the canon from the Apocrypha. None of the writers of the Gospels ever met Jesus (If you believe there was a person and not just a myth) The first was written at least 80 years after Jesus death, in the consensus opinion of most scholars (I am not one so I judge the sources.)
Actually the consensus date for Mark is 70-75 CE, shortly after the end of the first Roman-Jewish war and the destruction of the Temple. That puts it around 35-40 years after Jesus' death (usually dated to 35 CE or slightly later).
Even John, the latest of the gospels, is generally to have been written before the end of the First Century (95 CE is a common estimate), i.e. 60 years removed from Jesus' death.
I have no idea which scholars you've been reading but the above dates are fairly standard.
The consensus among scholars is that none of the authors of the Gospels ever met Christ and that the first was written after his death with Matthew, Mark, and John working from pretty much the same source material, and Luke playing Jung to their Freud