the manual and 1963 technical manual are a little vague on how you use the cleaning rod without dis-assembling the rifle. Was it originally designed that the weapon would be cleaned by inserting the cleaning rod from the muzzle?
Get a one piece stainless cleaning rod. Get a empty 12 gage shotgun shell.
Punch out the primer of the shell, drill the primer pocket to fit the cleaning rod.
Slide the empty shell over the flash hider. Now you got a rod guy.
NEVER used jointed cleaning rods. That screws up muzzles.
Never us coated cleaning rods, carbon gets imbedded in the coating and you effectively now have a file you're running in and out your barrel.
I don't like bore snakes for the same reason I don't like the coated cleaning rod. The bore snake also gets full of carbon and other crap I don't want in my barrel.
You'll ruin a M14/M1A a lot quicker with improper cleaning then you will by no cleaning.
Again, I'd recommend shooting your guy 5-600 rounds then worry about getting the gas plug out. I betcha it will come out easier then.
Beats twisting the gas system on the barrel.
Just basing this on my experience using the M14/M1A for over 45 years, 35 of that in heavy competiton. Which includes maintaining about two dozen M14s belonging to my AK NG Rifle Team.