Re: M1A stringing
This used to be a chronic issue with Garands. The upper handguard would swell and extend when it got hot, warping the barrel downward.
Unless you knew what to look for, it could be very frustrating. Trimming about 1/16" off the upper handguard's length so it would float fore and aft cured this issue as a generic fix.
No idea if this is your problem, but your post twigged the memory.
Also, M1/M1A/M14 bedding, as I was taught, involved setting it up with a small downward flex preload in the barrel, to eliminate vertical strings. The manner of function the gas system employs tends to accentuate this, and the preload tends to cancel it.
You can test for this by shimming between the front band and the underside of the stock relief that fits into it. This temporarily estabishes a preload and may also pinch the barrel and stock together, ala a barrel pressure pad.
The N/M flash hider has a reamed forward opening to prevent bullet strikes, which might be aggravated by a loose hider. I would not count on this as a permanent fix, but it can serve to motivate one to seek a more proper bedding job.
Some of this may be Rube Goldberg; but when we did it, it worked.
Greg