Obviously, I managed to push a few buttons!
I agree that the story of the blind men and the elephant works best. That's why, insofar as I know, it's the "standard." The Yellowstone fable works along the same lines, only with a more heavy-handed comedic tone. Like all fables, it breaks down if subjected to "objective" analysis. Fables deal in broad strokes, not particulars.
Differences matter. We agree. Still, I suspect the modern era (the past few centuries) has taught most of us to analyze and define most everything in terms of differences. I think this works well for science, and it's a handy tool for almost any academic discipline. It's been quite useful for biblical scholars as well. Still, I wonder if we have not become so conditioned to pounce on differences that we sometimes forget it might be as well to start with something as it is.
Take a good story, for example. The first thing to do with a story is to hear or read it as it is, to enjoy and respond to the whole, to allow it interface with your imagination as it may. Later, perhaps, there may be good reason to play the critic. While doing so, we may discover or guess at the origin, writing process, and editing of the story. We may even suggest how the plot, character development or dialogue could be improved. Critics, of course, face a particular danger: they may lose sight of the story itself. I'm not picking on critics (I am one!) but instead merely stating the obvious: all disciplines carry within themselves their particular temptations and dangers. Biblical criticism is not exempt.
As for the human capacity to witness the same event yet report it in wholly different fashions, I suppose we simply disagree. After 34 years of speaking several times a week to people who have come to know me well and who listen with some attention, I continue to be amazed at their diverse memories. They tend to hear and see everything through their personal filters, including not only basic content but even setting, body language, and intent. Their memories sift through and select pieces of a given sermon or lesson, and they organize their memories in ways that may or may not accord with my memory of the sermon event!
As for Mark, John and even Paul, I'm not certain it's correct to say they know nothing of the sermon simply because they do not deal with it per se. We could go round and round over whether or how the three incorporated insights from the sermon into their works. For example, I think 1 Corinthians 13 probably owes a great deal to Paul's reflective assimilation of the sermon, which then spills out "in his own words."
All of the above leads me to choose to try to deal with the story of The Sermon on the Mount as we receive it in Matthew, even as I make use of Luke's own version as a supplement. When I focus on Luke's account (sometimes called The Sermon on the Plain), Matthew becomes the supplement.
Great fun! Looking back over this entry, I suppose I must say that you managed to push a few of my buttons as well!