After reading the whole story, I got the impression that I had been to this repair myself... And I had a similar case 2 days ago. My minibus began to start badly "in the cold". And when it works a little, it starts up perfectly. There was an opinion that somewhere it sucks air into the diesel engine. They searched for 40 minutes(the electrician was also checked), but they did not find the reason - it was already late in the evening and the repair was closing