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Is it actually a heavy (Varmint Special) barrel? I can't tell from the picture.
In the first place, the "M" date code would actually be 1992 and not 1965. The "C" prefix to the serial number and the stock style are also dead giveaways that it's not a rifle from the 1960s. The "C" prefix was used in the late 1980s and I'm not sure if it was carried over into the 1990s or not. Typically they used a different letter prefix for about 5 years of each decade. The "A" prefix was used in the late 1970, "B" in the early 1980s and "C" in the latter 1980s.
In 1992, Remington chambered their Limited Classic for the .220 Swift. And, according to the catalog of that year, there were no other rifles chambered for that caliber (either in BDL or Varmint Special).
M - 1992 - 220 Swift - 7594 (number produced)
So, I don't know for sure what you've got there. If it's NOT a heavy barrel, it could be that someone restocked a "Limited Classic" with a BDL stock. I also can't find that it was chambered in a heavy barrel.......at least around that time frame.
http://www.remington.com/products/archi ... l-700.aspx
Den