FWIW:

The OP's Krag appears to have an aftermarket 'molding-ring' installed. This streamlines the 'step' between the barrel and front edge of the receiver.

Does the mounting-ring at the front of an S&K mount, for the Krag, go around the barrel or around the receiver?

The molding-ring may need to be removed to install, if the S&K mount-ring goes around the barrel, but, probably enough wood has already been removed in required area.

If the ring goes around the receiver ring, wood will likely have to be removed.