1990 I bought a 1943 IBM made M1 Carbine reimported from South Korea with all the post-WWII upgrades. Apparently the person for whom the dealer had ordered the gun did not consider it collectable* so I got it for a fair price. Over the years I acquired a Ramline synthetic sporter stock and an Italian repro of an M1A1 folder stock. I have shot it a lot participating in local military rifle matches over past two decades.
I got a repro of the US Army/USAF Tech Manual on Carbines M1, M1A1, M2, and M3 from the local GI Joe's Army/Navy Surplus store. Following the tech manual on the proper fit of the recoil plate to receiver for proper tension takes patience but is rewarding. I also followed their instructions on disassembly, inspection of parts for fit and wear, and reassembly of the M1A1 folder and made it tighter and less likely to fold unintentionally.
The CMP also has instructions on-line for fitting the recoil plate and the handguard for proper tension. That can improve accuracy. The handguard, though, should move a little, should not bind too tightly, but should not rattle either.
The rear of the handguard fits the receiver via a metal plate held in the handguard by rivets. Are the rivets loose?
The wooden lip at the front of the handguard fits into the flange of the barrel. Has the wood been worn or compressed?
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*Mix-master correct for Korean War/VietNam era (stamped and brazed trigger housing typical of IBM made M1 Carbines, parkerized postwar refinish, flip safety, 3-tab 30-rd mag catch, adjustable sights w. stamped base, and oversized M2 stock which I now suspect was by Howa of Japan for US occupation forces since it had a very rough non reflective finish). I first considered it (a) a collectible for 1950-1960s and (b) a varmint gun for up to 100yd.