Doesn't this actually work against your broader argument?

If the parables are easy to remember and pass down, then it means that people could very well have been playing telephone - albeit pretty successfully - with respect to the parables.

But it means that other aspects of the Gospel that weren't in parable form may not have been passed on so successfully as the parables.

It's my understanding that most Bible scholars believe that Matthew and Luke were based on Mark. So the drift you see between those three gospels is a pretty good demonstration of the game of telephone being played, and how much drift you culd expect to see over the years.