'Baltimoreed' - Boy, I'm glad the seller came down $45 on this wreck!
A truly fine looking Krag. I'm glad you were able to see past the heavy coat of cosmoline.
FWIW - I don't doubt the authenticity of your cartouche and script "P" stamps. Some 'J.S.A. cartouche' examples show rounded, rather than beveled, corners. There is a faint hint of a 'ghost cartouche' where the Die may have bounced after the cartouche was originally struck.
(The small "V" is a stocker or sub-inspector mark).
During the 'rebuild - process' stocks were scraped and lightly sanded to remove nicks and minor blemishes. That would explain any light areas of the J.S.A. initials.
(The box outline and circle outline may have been cleaned up and traced a bit, with a pick or metal brush).
Your forearm's 'finger grooves' look very crisp. The 'flame blue' of your extractor is correct.
BTW - The 'slotted' front-band was adopted in 1900. This might be a clue as to when your Krag was likely 'refreshed'.