John,....I'll bet with a little research about creating old looking finishes on guns, you could learn how to strip that new bluing off and create an "antique" looking surface,...just like it probably did look awhile back. You could experiment with a run of the mill clunker gun first.
There's some discussions on various forums around these parts where some experienced gunsmithing/ refinishers share methods for doing this. If you ever get a chance to have a look through a book titled "Metallic Cartridge Conversions" by Dennis Adler,...you'll see some great work by a gunsmith R.L.Millington,.....who has put some mighty fine looking "old" finishes on his contemporary cartridge conversions.
Just some thoughts,...so as you won't feel you have to be "stuck" with that new bluing on that fine ole Remington.
Ironically,..if it hadn't been re-blued,...you probably couldn't have bought it cheap.