Headspace that is excessive by SAAMI standards is quite common on these rifles (or even GI M14s). If the bolt only just barely closed on a NO GO gauge, it probably won't close on a Field Reject gauge, which is the real SAAMI maximum. There is no known case of one of these rifles failing solely as a result of excess headspace.
Your rifle is fine as-is, but if you want to tighten up the headspace for brass life, fitting a GI bolt is the way to go. As long as the headspace is less than .010" over minimum (as it probably is in your case), you can still get away with full-length resizing without overworking your brass. The alternative is to work around the excess headspace by neck sizing only with brass dedicated to the rifle.