This is not a high pressure pump problem. The engine management system on a common rail diesel will not even trigger the injectors unless the pressure in the fuel rail reaches a pre-determined point, so the fact it starts and runs when being primed suggests the high pressure pump is healthy. The problem is with the delivery of fuel to the high pressure pump, so will be somewhere on the low pressure side. It will be either the lift pump itself, or an air leak somewhere between the lift pump, and high pressure pump inlet.
You could confirm this by disconnecting the fuel inlet to the high pressure pump, and rigging up a clean container with clean diesel in it (cleanliness is critical) directly into the high pressure pump inlet. Hold the container above the pump so gravity does its stuff, and I bet the van starts and runs fine.
Don't disturb anything on the high pressure side at all. The unions on the pipes are single use, and if they are even slightly disturbed, the pipes need replacing. The pressure in these systems is phenomenal, and any escaping diesel could be under such pressure that it would be not only invisible, but capable of penetrating your skin and getting into your bloodstream. It is not melodramatic to state that if this happened, you wouldn't make it to casualty. Play around on the low pressure side by all means, but leave the high pressure side to the pros. And once again, cleanliness is critical on modern fuel systems.
Good luck!