IIRC there is a thing that may be needed when you reassemble the M1A…
has to do with the front portion where the barrel and stock come together…
the metal piece which is rather thin and springy that is kinda lose on the barrel needs to be pulled back toward where it will mate up with the stock… IIRC when they are mated there should be about 24 lbs of pressure there???
when I was in the military and we went for quals (boot camp) at the ranger we were told to NOT disassemble the rifle…
thought that was odd… but once I saw the diagram and the amount of pressure on that connection…
it all made sense… also notice a tool that looked odd when I picked up a rifle for quals… later on…
had a rather long handle and a u shaped section on the end… hard to explain but the u shaped piece had two odd prongs that bent back onto the u… figure that was for pulling the piece on the M14 back???
item 22 ( kinda hard to see)
this is a btter picture of the part I’m referring to

you should have a good solid fit there with the stock when reassembled no slop!
supposedly that reduces your shots going all over and often results in very tight groups???
