The SRS citation means Company "I" (eye, not 1) 4th U.S. Volunteer Infantry.

The initials on the butt-plate are absolutely not military in origin. The soldier would have been in a world of hurt for defacing government property.

Field-replacement stocks will have the (P) but no master armorer's cartouche. It occurs to me that perhaps an arsenal installed 32" M99 pattern stock on a legitimate M1898 Carbine, might also lack this mark. There would be supporting rationale/evidence both ways.

Interesting that the original low M96 carbine front sight (required for the M96 sight on the 98C when first made) blade was not replaced. This can also be a good or bad sign, depending on how you look at it.

5002 M1898 carbines were made, with short (30") stocks, saddle rings, and M96C sights. The stocks are identical to M96 stocks except for bolt notch and cartouche, which was always "JSA/1898". Very shortly after issue, they were supposedly all restocked. So, a short-stocked 98C today, is always suspected of being a reassembly.