As your MG34 was set up for, and fires 7.62x51mm ammo well, what I am seeing in the photos could possibly be one of a few issues:
1: Almost looks like not enough recoil of the bolt-assembly to get the bolt-head behind the cartridge-base.
What do the deformed cartridges look like on the front-half (?)......and are they hitting the barrel-face (?).
2: I would say that the cartridge-depressor in the top-cover is not holding the cartridges down......"but" you say it fires live 7.62x51mm ammunition well.
3: The issue that you sorted out on your MG42 using DAG Plastic-ammo/training rounds was the adjustment on the DAG Muzzle-Device......correct (?) Barrel needs to be fully forward for loading/operation. Possible look at this as a source of the same operational issue (?).......or a slow/dirty/weak-spring in the Barrel-Return-Mech. (Rod and Spring).
US Army, RET