On my poor bubbafied Krag, I can make out a serial number of x1916, with x being where a screw hole has wiped out the first digit, and nearly all of the number one.  However, thanks to the serial number lookup on oldguns.net I have narrowed down the only likely serial numbers to be 31916, 41916, 51916, 61916, 71916, or 81916.

Assuming I did my research correctly, 1896 and 1897 production are the only two years a Model of 1896 carbine would have been made, and these are the only serial numbers ending in 1916 that cover the range of 1896 and 97.

Having gone this far out on a limb, is there anyway of perhaps narrowing this number range down to carbines vs rifles? Right now it appears that there is a one in six chance one of these numbers are mine, and based on the production numbers I saw, statistically about two of those would be a carbine. 

Long shot I know, but if anyone could work some magic on serial number checks, I'd really appreciate it. Thanks!

Ahh, three down.  Might I ask how you were able to narrow them down?

Well, I neglected to ask about presence or absence of "Model", so, you are absolutely right about 3.

And, I spoke too fast as regards 7 (amongst a bunch of carbines) and 8 (which is all rifles).

There is no hit on either, but I'd have to put my money on 71916 at this point (probably about 99%).