Remington made barrels and sold them to gunsmiths. Apparently the barrel was worn or the owner dissatisfied and had the barrel bored out and recut.

What you described is a target rifle from the pre-cartridge era. The hole in the front isn't for a bipod (they didn't exist in those days) but for a barrel rest. It's a flat but has a corresponding stud that mates with the hole in the barrel. Using it ensures that your gun is horizontal (remember a slight cant can throw your ball off the mark at long range). That it doesn't have a telescope (they called them telescopes and not scopes in those days) doesn't mean that it wasn't used by either the side as a specialized sharpshooter rifle.

Various civilian target rifles were used by both sides during the war. However, their use was infrequent and most of the ones that saw service with Berdan's Sharp Shooters were sent home during the Peninsula Campaign. Still, some remained with them and various other units and the heavy barrel target guns remained in use up to war's end (I've been doing research on it for years). There are also accounts of target guns being used by the Western Army (Union).

Because ammunition was customized for each gun, the gun came with a bullet mould, swage and in most cases a false muzzle and bullet starter. Loss of these accoutrements could mean that the gun was no longer usable. You should check the muzzle for four holes to see if it took a false muzzle.

Now, as to whether your particular gun was carried by any soldier North or South, that depends on the provenance. Any papers or family history accompany the gun. Any former soldiers in the family line who served and in particular, any shooting awards? Not that there were medals (these were made privately in the Civil War days) and the winner could bring home bacon (literally) or beef or old fashion prize money.