The good news is that every thing you have posted so far points toward a carbine. A '96 rear sight would be correct and the serial # is in the possible range. The sling bar and ring are correct for a short forend stock. Does your front band have a hump to protect the rear sight and does it butt up to the sight?
The bad news is that with out documentation no one will ever be certain. Unfortunately the serial number range is only that, a range, as some rifles are known to be mixed in. If yours falls in a block of carbines the chances are better for you, don't have my list with me so I can't confirm or deny that.
Sounds like a nice piece though, do you know any history behind it or it's previous owners?