I doubt anyone will venture a specific opinion without a full set of pictures, including me. The issue is condition. The OP describes the gun as being in high condition, but that may merely mean high "Mechanical Condition", not the "Original Condition" of the finishes which would determine approximate value. This is also a Field Grade gun with steel barrels. True, the E Remington guns are more scarce than the later Remington Arms ones, but it's a matter of remaining original finishes. The gun could be anywhere from a few hundred dollars and up.

Please post some pictures, but I wouldn't count on having found a "Gold Mine".

Regards
Ken

I prefer wood to plastic, leather to nylon, waxed cotton to Gore-Tex, and split bamboo to graphite.