I offer one I believe is a 1899 altered for knife bayonet and sling and a school gun.  I believe it is real, and invite expert criticism.
1. Ser. 342910 is a 1899 (over stamp 9).  I sent an inquiry to Martial Arms Collector (SRS).  The response in Dec 2015 issue was over stamps were rare and all 1899s were carbines.
2. Poyer on page 101 discusses the over stamp 9 on 1988s to create carbines.
3. Barrel is 22", properly crowned.  Turned down in the modification to .620" back .75" to the properly mounted Krag front sight.  Fore end lightening hole professionally plugged.
4. Rear sight is 1898 carbine sight marked with c on base and eyepiece.  Only used on 1899 carbine (Poyer p 163)
5. Two cartouches, well worn, can't read.  One the normal dimension, the other more rectangular, perhaps a referb.
6. Wear on the for end stock and barrel blue reflects a lot of drill field time at parade rest and attention.
I offer it up for comment.
Joe

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IMHO: This could be a real 'School Rifle' (shortened rifle adapted for bayonet and sling). The second cartouche makes the stock alteration more convincing.

The front sight blade and pin look kind of funky.

The most significant thing to look at is probably the front barrel-band/bayonet lug.

Has the barrel-band been stretched on an arbor to fit the larger barrel contour?

How is the bayonet lug shaped?

The photos do not show detail of front band.

Sorry about the front sight.  The barrel band on this carbine is taller (1.360") than the one on my 98 rifle (1.302").  Hope the photos help analysis.  Also added the one I believe is student wear.

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Hmmm, I dunno. Some good, some defintely questionable.

Ignore the sight blade, that's a red herring.

Stock appears "nicely" but I'm not sure "properly" plugged. The band fit, however, does not appear to be of SA quality. The bayonet lug is wrong (not beveled).

Use of the M1898C (rare, and a nice find) is highly questionable. They were scrapped long before the school guns were made, and would be incorrect for that s/n range to boot.

The non-standard second cartouche is VERY interesting. Could we be looking at least a portion of the very first "real" PCR, and NOT a school gun, or a bubba, at all?

This one's a puzzler. Needs some more head-scratching.

Good observation Dick Hosmer on the 1898 carbine sight. On the first photos, I took it to be a 1902 sight.  There was not enough detail.

I would like to see a clear photo of the rear sight's eye-piece.

The additional photos reveal the front barrel-band to be pretty bogus looking and not  Springfield quality in fit to wood.

Still, a nice collection of Krag parts and an interesting Krag to study.

Here is the eyepiece.  Not sure what bogus front band means or a bevel on the bayonet lug.  Other than wear and being taller than the one on my 1898 rifle they both look the same.  I put it out on the forum to learn

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'HeyJoe' - It looks like a correct and complete model 1898 carbine sight. The front sight mounting screw looks bogus.

Things like incorrect sçrews , replacement sight blades and pins, make me suspicious of a Krag's legitimacy.

The front barrel-band, as altered for Constabulary and School rifles, is something I don't want to discuss too much. I don't want to be a 'Guide for Fakery'.

Suffice it to say, it was intended to accept the 1905 bayonet developed for the 1903 Springfield.