Your battery voltage is very low, it should have 12.6 volts when not running.
Have you checked current drain from the battery, with an ammeter when not running? It shouldn't be more than a couple of hundred milliamps when everything is switched off.
If you could beg/borrow/steal a clip-on ammeter, then you could check how many amps are flowing through the battery leads when the engine IS running simply by clipping the meter over the top of the lead
I still suspect the alternator diode pack, personally

Have we established which engine is fitted to the van?