Your M/12 was almost certainly made in 1910.
Sorry, but it ain't original for several reasons. I'll try to keep the story short... Rem got together with Fred Routledge in the 1930s and worked a deal to make the "Routledge" bores. They were first used on the M/121. Fred was in diapers, or nearly so when your M/12 was made. Also, the Routledge bore guns did not have rifling in any part of the barrel. Rem did not use barrel codes when your rifle was made. The "3" in the barrel code you show says that the rifle was returned for repair in October 1944. The barrel probably is original to the gun, but someone has played with it at a later date.
Model 12 with Routledge barrel mystery EDITED
Re: Model 12 with Routledge barrel mystery EDITED
That's probably what happened... The other letters, symbols are various testing/proof/inspector stamps. There's no way that I know of to tell who or what the stamps mean.
Re: Model 12 with Routledge barrel mystery EDITED
When I was doing the research for the Rem 22 book I owned nearly twenty Routledge bores. None of those had rifling... As I remember, the muzzle was .400".