R. Marshall,
The serial number 368 falls into an area that is not especially firm, as to date of manufacture. Number 356 is thought to be from 1898 and 950 is estimated to be from 1899. Between these two numbers, no others have been attributed to a date( as far as I know).Many early actions are dated on the receiver ring, but yours has a clawmount base dovetailed into it, removing any date. Therefore 368 falls between 1898 and 1899 as it would if it were 868.Of course 368 is closer to 356 than 868, therefore would be closer to 1898 than 1899.
With regard to the caliber of the rifle, I believe it is not 6.5x58 Port. because that cartridge has noticeably more taper in the body and shoulder. Between 6.5x55 and 6.5x57, the differences are not so obvious. A chamber cast will always be larger in diameter than the cartridge, and a chamber cast from a bolt action rifle doesn't accurately indicate case length because of the space between the rear of the barrel and the bolt face; in opposition to a rimmed cartridge in a break open gun were the face of the rim can be located. In rebarreling several Mausers, in can say the distance between the rear of the barrel and the face of the bolt varies. The last one I did measured .102"(2.6mm), by my faulty memory. When added to the 54.38mm length from your chamber cast this would result in a case length of 56.98mm. This is too long for a 6.5x55. The head diameter of the chamber cast is shown as 12.30mm, the head diameter of a 6.5x55 is about12.04mm(about .010" smaller), and the head diameter of a 6.5x57 is about 11.86mm( about 0.17" smaller).For both cartridges, the difference in head diameter of the cartridge and chamber cast is within often encountered tolerances. Based on mainly my rebuttable calculation of case length, I think it is chambered for 6.5x57.
Mike