Did Judas Historically Betray Jesus?

In my last reading of volume 3 of John Meier's A Marginal Jew: Rethinking the Historical Jesus, Meier defends the historicity of Judas' betrayal of Jesus.

Meier believes that the tradition that Judas betrayed Jesus is multiply attested by independent sources----Mark, John, and the different accounts of the death of Judas in M (Matthew 27:3-10) and L (Acts 1:16-20). In what I read, Meier did not refer to I Corinthians 11:23, in which Paul mentions an even earlier tradition that says (according to certain translations) that Jesus was betrayed. But perhaps that is another independent source for Judas' betrayal of Jesus.

Meier also maintains that the notion that one of the Twelve betrayed Jesus was embarrassing, and so the early church would not have invented it. Why, Meier asks, would the early church spend so much time exalting the Twelve, only to turn right around and invent a tradition in which one of the Twelve betrays Jesus? For Meier, it's more likely that Judas betrayed Jesus and that the early church then tried to explain that or account for it as a fulfillment of the Scriptures. 

Michael Cook, a professor of New Testament at Hebrew Union College (which is where I attend), offers different thoughts on the historicity of Judas' betrayal of Jesus. You can read them in this article here.

First of all, Cook maintains that there was development of the tradition of Judas betraying Jesus, which we can see when we compare Mark's skeletal account with the embellishments and attempts to explain Judas' betrayal that we see in the later Gospels.

Second, Cook does not believe that the tradition that Mark inherited even named Jesus' betrayer, but that Mark named him "Judas" to pattern him after the Old Testament figure of Judas, who was part of a body of twelve and betrayed Joseph for money (Genesis 37). Cook has stated that this sort of activity occurs elsewhere in the development of the Judas tradition. For example, Judas hanging himself in the Gospel of Matthew sounds a lot like Ahithophel, who betrayed David and hung himself (II Samuel 15-17). For Cook, Judas was being modeled after figures in the Hebrew Bible.

Third, Cook does not believe that there even was a betrayal of Jesus. He argues that the word that many translations render as "betrayed" in I Corinthians 11:23 can mean "delivered up." Cook states: "when you look at the scope of his writings, every time Paul uses this word in reference to Jesus, he means that Jesus was 'delivered up to death.' With this new understanding, the Last Supper passage would actually mean: 'the Lord Jesus on the night when he was delivered up to death.'"

Cook maintains that the story of Jesus' betrayal by Judas was late, on account of passages affirming that each of the twelve disciples would sit on a throne governing Israel (Luke 22:21,30; Matthew 19:28). Why would those passages even make such an affirmation, if those who wrote them were aware that one of the Twelve betrayed Jesus? For Cook, we first have the exaltation of the Twelve, and, later in time, the story was invented that Judas betrayed Jesus. Cook can think of reasons that such a story would have been invented, e.g., to address a situation in which Christians were betraying each other to authorities. 

Meier responds to some of the sorts of arguments that Cook presents (only he does not refer to Cook specifically in this particular discussion, but rather to others who have made such arguments). Meier is skeptical about the early tradition of Jesus' betrayal not knowing the name of Jesus' betrayer, for the early Christians preserved so many names (i.e., of disciples, of Hellenist deacons, etc.). Perhaps, but there are also plenty of characters who are left anonymous.

Moreover, I think that Cook's analysis demonstrates the weakness in Meier's appeal to multiple attestation to support historicity, at least in this case. If someone invented a tradition that a person betrayed Jesus, and that was embellished by Mark, and M and L took Mark's story in different directions (with regard to how Judas died), and John embellished the story in his own way, then how are we dealing with independent sources or witnesses? Sources that are allegedly "independent" may be related to each other, in some way.