I have a Model 11 with the same safety as yours. Its serial is 249###. Remington dated it as 1923. The barrel codes dated it the same. The barrel codes began in 1921. Your shotgun is most likely predates the barrel codes.
Remington will date your shotgun for you. You can all 800-243-9700 Mon-Fri 9-5 EST or email their help center but you have to sign up with their site for that. You can also request owners manuals for your firearms. I've done this with a couple of my Remingtons, it's usually a photocopy.