But you don't know if the "K" on the barrel is the month code for May or the year code for 1963. The assembly codes ALWAYS consist of either 2 or 3 letter. If only 1 letter is present, that suggests that the barrel has been set back, because the year code letter has been milled off, and it is not an original factory installation.
Despite the 5-digit SN, I think that it would be very unusual for Remington to build a rifle in 1963/64 for a cartridge that they didn't introduce until 1969/70. But, as with many things, YMMV.
Jeff
