This is the solution to your problem. Milsurp brass comes to you having been fired in much looser military chambers. A full length sizer die will not size enough at the case head to fix this. That is why a small base die is needed.
If you take one of the loaded rounds that is giving you trouble and try to chamber it in a bolt action .223, you will be able to feel the bolt camming the round into the chamber. If it will, in fact, chamber at all. You AR has much less camming power to feed or extract your rounds.
Yes, you will need to pull your bullets and properly resize your cases with a small base die. This is a good example of why one should do careful load development when loading for semi-autos, including function testing, before loading large batches of ammo.