I don't remember how oil gets into that pump, whether the pickup tube bolts to the pump, or there's a passageway in the block from the pickup screen to the pump, but look for anywhere air could be drawn into the inlet side of the pump along with the oil. A leaky gasket where the pickup screen bolts to the pump is the most common cause, but a cracked pipe on the pickup could happen, etc. Just make sure the pump sucks up only oil, not air along with it!
Jerry