'chadaz34' - Welcome to the KCA Forum.

I don't know your source of information. It sounds like the "Bowers site" which is not to be trusted.
As far as I know, there is no validity to 1st model, 2nd model, 3rd model terminology for model 1899 carbines.

The model 1899 marked receivers were built into carbines. Carbine, #345302, was likely assembled around August to October, 1901. Krags were not assembled in numerical order. The numbered receivers went into parts bins and were rather randomly pulled out for assembly.

Carbines were produced periodically in batches.

There is a complicated story of sight-model changes to model 1899 carbines.

Your carbine, #345302, was likely built with the model 1901 carbine rear-sight and a regular 'cocking-piece' (and not, the knurled 'head-less' version). The original hand-guard was likely the same as that for the rifle with a 1901 sight.

Eventually a hand-guard with a 'lump' sight-protector was built for the carbine with the 1901 sight.

A model 1899 carbine could have had its hand-guard updated or its rear-sight and hand-guard updated at various times in its service.

Either a model 1901 or 1902 carbine rear-sight is credible on your model 1899 carbine. (There are 'sight specific' hand-guards needed for those sights).

In regards to your original question as to "value":

IMHO - most variations of the model 1899 carbine will be of nearly identical value. Condition of wood, metal, bore, and 'appeal of appearance' are more significant in fixing value.