Hearsay says the M or W makes it a Douglas barrel, but no proof has ever been given to substaniate it. Ditto with all the other barrel stamps on various TC sidelock barrels.
That's why you didn't get a difinitive answer at MLF despite the huge knowledge base there, and you won't get one here either. Nobody knows for sure. TC has never put any of the serial number/year or barrel maker data out to the public, and all their early records were lost in the plant fire. Like roundball I have worked for years trying to piece it together but even the pieces are just speculation. I can come up with what years the different models were offered accurately for the most part, but not what year a particular rifle was made by it's serial number or what any of the barrel stampings indeed indicate.
Just enjoy your fine production rifle for what it is.