If Paul can see a bright light on a dark desert highway and believe that he has seen the physically resurrected Jesus then it is entirely plausible that this is what happened to Peter, James, the Twelve, and the “Five Hundred”. They all saw a strange bright light and believed it was an appearance of the physically resurrected Jesus. Paul may have believed that his bright light spoke to him, but a guy who believes that he has taken an intergalactic space voyage to a “third heaven” to hear confidential communications between space people is not dealing with a full deck. The Gospels were written by non-eyewitnesses, decades after the death of Jesus, writing works of evangelism. The appearance stories in Matthew and Luke have nothing in common. Any non-biased reader would see these two stories are fictional embellishments of the bare-bones appearance accounts mentioned in the Early Creed. And John’s appearance stories, written one or more decades later, look like an amalgamation of Matthew and Luke’s appearance stories. Fleshed-out appearances stories involving seeing and touching a resurrected corpse are going to convert many more souls than a dry, non-descript list of alleged eyewitnesses.
Unlike Jesus’ disciples, Paul was a highly educated. He was also a Pharisee. Yet he converted to the new Christian sect due to a (talking) bright light. How much more likely then are the chances that the “unlearned” disciples converted due to even less dramatic experiences, such as vivid dreams, false sightings, or non-talking bright lights!
I can see how a skeptic of Christianity might be tempted to doubt Paul/Saul’s claim to have seen Jesus in a vision on the way to Damascus. His was a solitary vision, and our faith in the veracity of what he saw and heard is based on his own witness, so I can understand how a non-believer might be hesitant to simply accept his witness. For me as a Christian, I can see the result of Paul’s life, and I trust Peter, who called Paul’s writings “scripture” in 2 Peter 3:15-16. Also, I have been convinced that the entire New Testament is inspired, and that includes many writings of Paul. Therefore, for me, that Paul might have invented his vision of Jesus is not a rational possibility, but I can understand how a non-believer might feel that way.
However, to compare what Paul saw to what the 500 eye-witnesses saw or what Peter and the other apostles saw is to make a comparison when there is none. The apostles did not see a bright light. They saw Jesus. They talked to him. They ate fish with him. The veracity of these many dozens of witnesses is very strong, as all of them were willing to die for their faith. Why? Because they saw the risen Jesus. Your proposed idea that they were simply hearing things does not match with the data.
You accuse Paul of not dealing with a full deck. That is interesting because he planted churches all over the Mediterranean. He interacted with the most educated people of his day in Athens and did just fine. As to his having a vision of the third heaven, to the Greeks the sky is the first heaven, what we call outer space is the second heaven and “the third heaven” is the abode of God. Paul is simply claiming to have had a heavenly vision. I can understand your doubting this, but calling him crazy or not dealing with a full deck is not consistent with everything we know about Paul.
Two of the gospels were written by eye-witnesses–Matthew and John. It is true that Matthew wrote, probably in the 60s, but I can certainly remember quite well what I was doing 30 years ago. I assume you can as well, if you are old enough. Mark was probably an eye-witness to at least some of the events, but he was the companion of Peter, who certainly knew what Jesus said and did. John probably did not wrote until nearly 50 years after the events, it is true, but I have been a Christian for over forty years, and I am pretty sure I will still be able to remember ten years from now such important details of my life as John remembered about Jesus. If you want to accuse John of lying, that is one thing, but to imply that he did know know how Jesus died, the claims he made about himself, and whether or not he was raised from the dead, then this accusation does not work as far as I am concerned.
You say that the appearance stories in Matthew and Luke have nothing in common. Matthew 28:1-10 has quite a bit in common with Luke 24:1-12. Besides, these are separate accounts. The fact that Matthew does not record the scene on the road to Emmaus does not mean that it did not happen. These are independent accounts. If they reported the exact same information, what would be the value of having four independent accounts, which is what they are? The gospels are four largely (but not completely) independent accounts, from different perspectives. Luke’s account is the most carefully researched of the four because he was not an eye-witness, but we can assume from the context that he interviewed many. Unless you can show an actual contradiction (which you have not, at least so far) then the evidence tells me that the different accounts are separate but reliable accounts of what actually happened.
I am a rather skeptical person–being a PhD in chemical physics, and I have looked at the four accounts. I find them to be perfectly credible, and I find no reason to believe that John or Matthew lied about what they saw and heard. I believe that the reason Christianity spread like wild fire in the first century is that the tomb of Jesus was empty, because of common knowledge of Jesus’ spectacular miracles, and because of the historical fact that Jesus fulfilled such prophecies as Psalm 22, Zechariah 11, Daniel 9, Micah 6, Isaiah 53 and so much more. Jesus’ ministry succeeded because he was who he said he was–the resurrected Messiah. That is my take on the facts.