My best guess is a combination of issues.
1) I'll bet your barrel is out of index.
2) I'll bet your op rod guide is even more out of index.
3) The two above conditions are causing your oprod to "twist" your bolt as it cycles, causing the jam at the rear top right.
The bright side is there are fixes if I am right. The best fix is to have the barrel re-indexed at a gunsmith or M14 clinic. The temporary fix to get you shooting right now though, is pretty easy.
Strip the rifle so you only have the barelled receiver, op rod, bolt, gas system and opr rod guide installed. Make sure the stocks are removed including the handguard and also remove the operating rod spring and spring guide.
You will need a leather mallet or shot filled plastic dead-blow hammer. As you close the action in the above state, observe if the tip of the op rod is contacting the gas system piston dead centre. Chances are it is not. If not, use your dead blow hammer to displace the op rod guide axially left or right a couple degrees. You might have to whack it fairly hard. The object is to get the op rod guide indexed to the gas system.
The op rod guide is retained by a roll pin through a fairly loose tolerance groove in the barrel and there is about 10 degrees of potential play left and right without hurting the roll pin on a CHINESE M14. On a GI one, there is a little less play.
Now that it's indexed, with the rifle still in the above condition and UNGREASED, tilt the rifle forward and backward 30 degrees. The weight of the op rod and bolt should cause the action to open and close under their own weight at this angle and travel the full distance without binding. The one exception is the action might bind SLIGHTLY on the way open when the op rod is at the extreme rear position due to the bottom of the barrel causing *slight* friction against the top of the op rod scallop cut. It should NOT bind. If friction causes it to slow, it should still move freely with just pinky finger pressure.
Now, if after the above the the bolt is still binding at the rear, then the barrel is way out of index to the receiver. and you will want to re-index it. You can, however, move the op rod guide back out of index with the gas system until the bolt isn't binding, but this is only a temporary fix as you will beat up the op rod tip too quickly if you don't correct he root problem. You want the op rod tip to contact the full surface area of the piston to evenly distribute the force from cycling the action while firing.
Hope that helps.
Can I whack this with a mallet?
