Mike357 - hay pal, you're shooting ammunition that may be over 40 years old. Some of those rims might well be thin or you just might have a crummy batch of ammo. There's nothing to say that just because the headstamp is from Lake City it is the best there ever was.
If you can drop the empty case out with a dropped cleaning rod then one of two situations may be suspect (1) crummy or old ammo with thin rims that your extractor just rips the head off or (2) fired cases that stick in the chamber due to higher pressures (for whatever reason) and the extractor just rips the head off - you can drop them out with the cleaning rod because in the time it takes to put the rod down and drop the case, it has cooled enough to take some of the pressure off.
I would try some newer ammo first before I do anything else. Also, see if you can e-check with the Lake City Arsenal to see if they had a recall out for any of those lots of ammo. Hope this helps. Mikey.