Contradiction: Where was the Risen Jesus First Seen?

This is partly in response to a post by Joe Hinman, which in turn was a response to a comment I made on his blog.
http://christiancadre.blogspot.com/2019/12/real-contradiction-in-resurrection.html

The question is whether Jesus was first seen in Galilee or in Jerusalem (and surrounding area) after the crucifixion. Mark says it was Galilee, the later authors say it was Jerusalem.

Bear in mind it takes about three days to travel from one to the other. We can suppose that Jesus was miraculously in two places at the same time, but not Peter (or the other disciples). If Peter saw Jesus in Jerusalem on that first Sunday, he simply cannot have seen Jesus in Galilee on that day too.

Mark

Mark says Jesus intended to go on ahead to Galilee, and see the disciples there:

27 And Jesus *said to them, “You will all [k]fall away, because it is written, ‘I will strike down the shepherd, and the sheep shall be scattered.’ 28 But after I have been raised, I will go ahead of you to Galilee.”

And that is what happened:

Mark 16:7 But go, tell His disciples and Peter, ‘He is going ahead of you to Galilee; there you will see Him, just as He told you.’”

Luke and John

Luke is very clear that the disciples were in Jerusalem when the Empty Tomb was found, and that very same day Jesus appeared to the disciples:

Luke 24:13 And behold, two of them were going that very day to a village named Emmaus, which was [d]about seven miles from Jerusalem.
...
32 They said to one another, “[k]Were not our hearts burning within us while He was speaking to us on the road, while He was [l]explaining the Scriptures to us?” 33 And they got up that very hour and returned to Jerusalem, and found gathered together the eleven and those who were with them, 34 saying, “The Lord has really risen and has appeared to Simon.” 35 They began to relate [m]their experiences on the road and how He was recognized by them in the breaking of the bread.
36 While they were telling these things, He Himself stood in their midst and *said to them, “Peace be to you.”

Similarly John insists it was that same day:

John 20:3 So Peter and the other disciple went forth, and they were going to the tomb. 4 The two were running together; and the other disciple ran ahead faster than Peter and came to the tomb first; 5 and stooping and looking in, he *saw the linen wrappings lying there; but he did not go in. 6 And so Simon Peter also *came, following him, and entered the tomb; and he *saw the linen wrappings lying there,
...
19 So when it was evening on that day, the first day of the week, and when the doors were shut where the disciples were, for fear of the Jews, Jesus came and stood in their midst and *said to them, “[b]Peace be with you.”

A Contradiction!

Either the disciples, and more specifically Peter, believed they saw the risen Jesus first in Galilee or in Jerusalem. One of these must be wrong. Which one?

And how did the author get something so fundamental to the faith so very wrong?

Is it plausible that Mark had not heard of the Jerusalem appearances? According to tradition, Mark was Peter's secretary (even if Mark was not the author, the gospel is generally believed to have been written in Rome, where Peter was bishop and the same argument applies), so we have to question whether Mark would have heard from Peter the events in Luke 24 and John 20. Is is plausible that Peter never mentioned to Mark that he was one of the two disciples who found the tomb empty? Is it plausible that Peter never mentioned Jesus appearing to him and most of the other disciples that day? No. This was the most important single day of Peter's life and there is no way Peter would not be talking about it endlessly for the rest of his days - if the Gospels of Luke and John have it right.

The only plausible answer is that Luke and John are wrong. Mark did not mention the appearances in Jerusalem because he had not heard of them, and the reason he had not heard of them is that they had yet to be invented. They were made up some time after Mark was written.

In fact, if we look at Matthew we can see an intermediate step in the evolution of the story. In Mark it all happened in Galilee, while in John and Luke it all happened in Jerusalem. In Matthew, however, Jesus is seen briefly in Jerusalem by the women, and later in Galilee by the disciples.