It fits exactly in the way that I've seen about a half dozen others. The others that I have seen, several had RA-P stamps on the stock. They also were stamped with the last four in the handguard and stock like this rifle. several also had receiver sights on them. One of them had real DCM paperwork as being sold out of Odgen arsenal I believe in the 60's, or some Army Arsenal.
I really think as I said, especially now with seeing these additional pics, that this style of rifle was some type of target rifle rebuild program that was post Korea. My hunch is the Marines kept their NM And special target seperate and turned them over to the Army probably notating they were Match rifles.
Then the Army rebuild them again as target/range rifles. That's just been my hunch and your's just fits the narative exactly as I've seen others.
Usually these rifles will also have a serialed bolt. But a weird serialed bolt. They grind off a bare spot on the top of the parked bolt and eletric pencil the serial on it. Probably because it's hard to get a electric pencil to arch on a parked bolt without taking the finish off.
I know I talked about this style of rifle years ago I believe on this forum. Let me see if I can find the link. It was to three of them. Two of which had the star, but all three, and now yours have the same traits.