After a month of investigation, here is my working hypothesis on what's called "the synoptic problem". This is how I suspect the Gospels of Mark, Luke and Matthew were composed.
In one sentence: Matthew took notes during Jesus' ministry, which Mark and Luke used to write their gospels (in turn) before Matthew finally used his own notes (and other sources) to compose his full Gospel.
Now here is the shortest summary I can write about how that might have happened in real life:
From 30 to 33 AD, Matthew took notes during Jesus’ ministry and filled in earlier details by interviewing Jesus and the other disciples. Matthew held onto his notes as a collection for many years and several copies were made. The collection was never well organized, but Matthew felt like it was a good record of the events. He did not modify the form of the collection for nearly thirty years. Matthew did, however, begin to keep private notes about his personal studies of scripture.
From the Resurrection to the Council of Jerusalem (17 years) the early church did not experiment with literary opportunities, other than making some copies of Matthew's notes. Basically, they all thought that was more than enough. But when Jerusalem decided to send a letter to all Gentile churches, at least three men were suddenly inspired to think about the power of literature. One of them was Mark.
Between 50 and 53 AD, Mark got a copy of Matthew’s notes and sat down with Peter. Peter gave Mark extra details and supplied the basic sequence of events. Mark chose to keep things tight and skipped over many of the longer sections on Jesus’ words and teachings. But Mark also put in anything Peter wanted to add, including a few stories from Peter's own memory.
In the mid-50's AD, certain Pharisees had been persuaded to believe in Jesus’ teachings, but not his sacrifice or resurrection. Some of these men used copies of Matthew’s notes AND copies of Mark’s Gospel to begin composing their own “sayings gospels”. A few copies of these were being passed around Israel by 57 AD or shortly after.
In 57 AD, after Paul’s arrest, Luke decided to write a defense of Paul and of Jesus, “whom Paul was preaching”. Luke quickly learned that many others had begun to write accounts of Jesus’ life and/or teachings – though not all who began such a task had completed it.
Luke got a copy of Matthew’s notes AND a copy of Mark’s Gospel. Luke found and read the “sayings gospels” but they did not significantly impact his work. If anything, these collections may be what motivated Luke to expand his writer’s purpose beyond a simple defense of Paul. Luke used Mark’s Gospel as a basic framework but chose to include pieces from Matthew’s notes that Mark had left out, picked over or modified.
Luke also interviewed many eyewitnesses and included snippets about them. Luke’s second “book”, of course, rested almost totally on personal and eyewitness testimony, although Matthew’s notes may have had bits on the very early church in Jerusalem. Luke also made many other decisions about what to include or leave out that each suited his peculiar ambitions for the complex purpose of this unique undertaking.
In many ways, Luke was far more dynamic as a writer/editor than Mark had been. But Matthew was about to prove himself somewhat dynamic as well.
Matthew finally converted his own notes into a complete Gospel sometime after Luke sailed from Caesarea (59 AD). Matthew's main source was his own notes and some new research, including three decades of personal study in the 'Old Testament' scriptures.
Matthew did not rely on Mark's Gospel because it was secondary to his original notes. However, Matthew had certainly seen Mark's gospel and may have been influenced by it in some ways. For one thing, Matthew probably made the deliberate decision to compose a different sort of work. (Otherwise, why publish at all?)
Matthew did not use Luke's Gospel as a source because it wasn't complete yet when Luke sailed out of Judea. But Matthew must have met with Luke at some point. During the two years Luke vigorously sought out both written sources AND eyewitnesses, Matthew was the one man who ranked most highly in BOTH categories! Therefore, assuming Matthew was anywhere in Israel from 57 to 59, he absolutely had to be Luke's chief "get".
So Matthew and Luke got to exchange new research and information not found in Matthew's original notes, such as details about the Herods and the early life of Jesus. They met together at least once. Matthew and Luke could easily have swapped much research on the same topics when certain details were more fitting to one man's goals-in-writing than the other's.
Matthew also had access to some "sayings gospels" but he did not use them as a source. Like Mark's Gospel, they were largely based on Matthew's own notes anyway. However, Matthew did use them as a reference for certain things he wanted to address in specific ways.
Matthew chose to alternate sections of Jesus’ teachings with sections on his life events. The long teachings sections were opportunities to draw in the interest of certain Jews while emphasizing the points Matthew wanted to make. But the sections on Jesus' life were crafted together thematically, to emphasize challenging points about Jesus Himself. Therefore, Matthew was careful not to use too much time-specific language in sections where he knews he was not being chronologically accurate, or where he just wasn't sure.
Matthew had finished his Gospel as early as 60/61 AD. By that time, he was easily more than 50 years old. Old age was partly what gave him the time to finally write and edit such a focused, carefully arranged composition.
Practically speaking, most copies of Matthew's original notes were thrown out as obsolete whenever the copies' owners got copies of the new and improved Gospels. But any surviving copies of Matthew's original notes were probably cannibalized for new "sayings gospels" in years to come, which continued to be popular in certain circles for quite some time.
But the Gospels were and are the best original sources on Jesus Himself.
This is my entire working hypothesis for the Origins of Matthew Mark and Luke's three Gospels, so-called as the "Synoptic" Gospels because they share the "same view" of Jesus in many ways.
There are many other considerations, but this is the simplest form I can put these ideas into, today. I'm hoping for some feedback, but I'll continue to do what I can if nobody wants to offer me any.
This is a hypothesis. It must have some problems. Or it might well be perfect.
Either way, now the real work can begin…