That Markan Priority thing-a late innovation.
I would say it best accounts for the data and doesn't innovate anything.
If Mark wrote first, he'd be first.
More speculation. Why is it necessarily the case that the gospels must be presented in the canon in the order in which they were written? Why aren't Paul's letters presented in the order in which they were written? Why is John not written chronologically?
They each wrote independently.
So did they miraculously land on verbatim wording in passages for large swaths of their respective gospels? I doubt it. Regardless of the particular solution to the synoptic problem, it looks obvious to me that someone was using someone else's gospel as a source.
Regarding Aramaic Matthew (not Hebrew as I previously stated...
Around 180 Irenaeus of Lyons wrote that
Matthew also issued a written Gospel among the Hebrews in their own dialect, while Peter and Paul were preaching in Rome and laying the foundation of the Church. After their departure, Mark, the disciple and interpreter of Peter, did also hand down to us in writing what had been preached by Peter. Luke also, the companion of Paul, recorded in a book the Gospel preached by him. Afterwards John, the disciple of the Lord, who also had leaned upon his breast, did himself publish a Gospel during his residence at Ephesus in Asia. (Against Heresies 3:1:1)
Fifty years earlier Papias, bishop of Hieropolis in Asia Minor, wrote, "Matthew compiled the sayings [of the Lord] in the Aramaic language, and everyone translated them as well as he could" (Explanation of the Sayings of the Lord [cited by Eusebius in History of the Church 3:39]).
Sometime after 244 the Scripture scholar Origen wrote, "Among the four Gospels, which are the only indisputable ones in the Church of God under heaven, I have learned by tradition that the first was written by Matthew, who was once a publican, but afterwards an apostle of Jesus Christ, and it was prepared for the converts from Judaism and published in the Hebrew language" (Commentaries on Matthew [cited by Eusebius in History of the Church 6:25]).
Eusebius himself declared that "Matthew had begun by preaching to the Hebrews, and when he made up his mind to go to others too, he committed his own Gospel to writing in his native tongue [Aramaic], so that for those with whom he was no longer present the gap left by his departure was filled by what he wrote" (History of the Church 3:24 [inter 300-325]).
I'm aware of the quotes (I think I recall saying I was aware of the theory, so I'm not sure what simply quoting the church fathers to me will accomplish). A few further notes though
(1) I have a few problems with the Aramaic idea. First, with the exception of Papias, the traditions you cite are later. Origen clearly states, via Eusebius, that he learned it from somewhere else. Why think that their source wasn't ultimately Papias? It seems this is the logical conclusion since Eusebius cites Papias and Irenaeus regarding this (in other words, counting Eusebius and Origen themselves don't actually add anything) and it's the earliest source we have of this tradition.
As far as the validity of Papias' statement, I think we need more evidence. We can't be sure that the gospel he was referring to was the "Matthew" in the canon or that he wasn't simply mistaken. And rather than think something along the lines of: well Papias heard John therefore...., it's worth noting that Papias doesn't state from where he obtained this information. So we shouldn't assume that he heard this specific piece of information from John himself.
Additionally, Papias' statement itself isn't unambiguous. Does he mean to say that Matthew wrote in the Aramaic language or that he wrote with an Aramaic dialect (which could mean that he wrote in Greek)? And when he "compiled sayings" does this mean the whole gospel or just part of it or just the sayings of Jesus..? Papias' statement could be read a few different ways.
I'm not against tradition, so I don't discount Papias as some might, but I don't think this is so clear as you try to present especially when considered with other reasons. Papias' statement requires further qualification and evidence. So, as I previously said, I wouldn't build much off of the necessity of an Aramaic gospel of Matthew, especially something that would be theologically central.
(2) We also have no manuscript evidence of an Aramaic original Matthew, which seems to be a significant point since we have lots of manuscript evidence.
(3) We also still have the synoptic problem which would seem to argue strongly for a Greek Matthew.
(4) I would also be curious as to why Matthew feels the need to translate "Eli Eli lema sabachthani" into it's Greek meaning? I mean, if "Matthew" is writing in Aramaic, for an Aramaic speaking audience, then why does he need to explain to them the phrase's meaning? Wouldn't it be redundant? Wouldn't it be redundant..? (
) Mark does the same, which makes sense if the audience doesn't know Aramaic.
The same is the case for Matt 27:33. Why the need to translate an Aramaic word? Maybe the case with Matt 1:23 as well.
We could also make a similar argument with Petros. If the Aramaic "Cephas" is so central to understanding this passage, then why don't Matthew or later redactors leave "Cephas" in the passage as was done with "Raca," "Golgatha" and "Eli Eli lema sabachthani?" Well, if word-play in Greek is what was intended to be understood, then you have your answer.
(5) Matt 9:24 // Mark 5:41 //Luke 8:54 tell the same story, but Matthew and Luke omit the Aramaic phrase. If Matthew was writing in Aramaic and to an Aramaic audience, why omit the phrase? If your audience is Greek-speaking and reading though, then you may do what Luke did or omit it as Matthew did.
I could probably come up with other reasons and maybe some other poster's could too, but I'm running out of time today....
You can't do that. The Gospels are a whole.
(a) I most certainly CAN do that. You aren't the boss of me
(b) I think that to best understand the gospels as a whole you have to let each author speak for themselves and understand them on their own terms. I think your method doesn't best take the author's themselves into account.