The safety lock you describe with "FIRE/SAFE" both in serifed letters (and marked "R" on the rear face) is not contemporary with your '03-A3's serial number. The safety lock comes from a much earlier rifle. The correct safety lock for your '03-A3 would have "FIRE" in serifed letters and "SAFE" in block letters.
The Remington reference book you seek is yet to be written. In the meantime, feel free to come here and ask.
J.B.