***Since from the text we learn the crowds followed Him up the mountain and then back down the mountain, it certainly seems likely He knew His entire audience.***
Knew His entire audience? What does that mean?
They didn’t have high powered speaker systems in those days; if one did not possess iron lungs and stand with arms and legs akimbo such as the Shakepearean veterans did, one would not reach the full extent of one’s audience especially if it numbered in the thousands. Sitting on a rock does not lend itself to audibility to the crowds.
Just as there are passages where Jesus speaks directly to Peter, with the others overhearing, thus Jesus speaks to His disciples, with those nearby overhearing.
I think the fact some people believe the Sermon on the Mount wasn't intended to be received by the ears of all believers is really really strange. Talk about elitism and exclusion.
I know movies aren't Scripture, but have you ever seen the movie, "King of Kings" with Jeffrey Hunter? It illustrates how Christ was speaking to the crowds on the sermon on the mount. And it didn't look like any of them had a problem hearing Him. It makes sense He would walk upwards on the mountain, in order to better project His voice to the eager throng who came to listen and learn from Him.