Wait for other opinions. Also see if the engine continues running with the oil cap off. As long as it is not puffing like a steam engine and throwing oil out.

If there is too much base pressure present in the engine from blowby it can shut the engine down. Acts internally to shut the injection pump off. Or try a hot restart with the oil cap off.

Personally I just still feel it is not the fuel injection pump itself. Still I hope the additional explanation of how an engine making too much blowby can shut the injection pump down is understandable. Easy to test and eliminate if nothing else.