Sounds like a Model 10 to me also. I don't know when Remington began marking the receivers with a model number but the serial number seems high to be an early model. Due to the alterations, it is possible the gun was refinished at some point and much of the original marking were removed in the process. The paddle lifter wears easily and is not available as a separate part. I had to buy two other Model 10s to repair the paddle. This got to be expensive as one had to fit a "new" but worn part to the gun.
My first 12 ga was a trap model I bought at a garage sale for $50. It came with a folder of newspaper clippings and a trophy as the original owner was a noted local trapshooter of the early part of the last century. It was eventually relegated to "old timer" preserve hunts where we took out the old dogs and used old guns and shells. Unless health reasons dictated, no dog was younger than 10, guns were pre-1950, and shells were factory papers pre plastic shotcup. It was a great time.