I spent a fair amount of time in college reading up on the basics of the Synoptic Problem and the various "German higher criticisms." My presumption was always Matthean priority, and I think that presumption was mostly formed by tradition.
In reading up on the various proposed solutions for the Synoptic Problem, I found that each one had a significant number of difficult counter-examples. None (even my favored) was air-tight. In reflection of those studies, I'd like to propose the following hypothesis:
No theory for the documentary history of the Synoptic Gospels can satisfactorily explain all of the data.
I don't think there is a solution to the Synoptic Problem.
Note that I am not saying that there isn't an objective truth about the documentary history of the gospels. One of the propose solutions is probably more or less correct. But I think that the tools of source criticism and its cousins are not sufficient too the task. There are simply too many variables, especially when textual criticism comes into play.
Perhaps we are better off that there is no solution, because I do not think it is a "problem" as such, except to textual critics.