"Jeremy" - You have a carbine barrel and correct 1896 carbine sights. Your action's serial number is in a 'known carbine range'.

It would be to your advantage to patiently acquire a correct saddle-ring & bar and an 1896 carbine barrel-band. (These parts in condition, comparable to the rest of your carbine, would cost about $200).

Look for parts that have some 'experience' and match the outward condition of the rest of your carbine's metal.

FWIW - Your carbine's rear-sight alone is worth around $500.

If fully completed with correct original parts, your carbine would likely be worth approximately $1,000 to $1,300. 

We haven't seen the ends of your stock. Hopefully, your bore is in nice condition and no one added a butt sling-swivel or altered the butt or forearm of the stock.

BTW - Don't 'refinish' anything or you will harm the carbine's value! You (and other collectors) want an honest carbine showing its age and patina.

Your stock, with its 1897 "Acceptance Cartouche", is likely original to your carbine. The 'Script' letters are "J.S.A.", for Joseph Sumner Adams, Foreman of the assembly room at Springfield Armory. The cartouche was applied to the stock when the arm was inspected and accepted for U.S. service.

p.s. - I don't have a model 1896 carbine, (yet). The Remington factory ammo has always been accurate in Krag rifles and carbines, that I fired it in. :)