If the Gospel writers were free to make changes this significant, then the Bible is not inspired. It is a work of fiction. Another explanation could be that Jesus did reverse the order because it was "in remembrance of Him". From then on, they would remember Jesus uniquely every time they partook.
One, that's pure speculation, although a "soothing one," and, two, it doesn't explain why the first century Christians in Didache reversed Christ's reversal, or why would they want to!
You are dismissing those Christians who lived in the time when Apostles still walked the earth. Could it be, perhaps, that it was because the Gospels were still being written at that time?
I would wager on that possibility, although it is not as "soothing" as your speculation. After all, the Gospels seem oblivious to Peter's Epistles and vice versa.