This is a complete WAG, but I've had a similar issue with the AMG 6.5L TD in my motorhome and the 6.9L NA in my Ford van.

The problem with the 6.5 - after replacing glow plugs (which were from the original engine, so they needed it), controller, and lift pump (which also was bad) - the culprit was ugly battery grounds on the engine.

The Ford's 6.9 had similar symptoms, but the problem with it was the injector return lines' sucking air when the engine stopped.