Once you confirm the delivery valve is ok, you can try doing the static timing test as described in the TM. This may show you if the plunger guide has skipped or not. I would assume that you will find the timing to be completely wrong if it has.
While you are in there, try doing a visual check to see if the plunger is both rotating and moving in and out as you rotate the motor by hand from the blower wheel bolt.
AND, just for giggles, look at the tag on the right side of the pump and see if it is an Ambac M-50 ( blue tag ) pump or an American Bosch PSU ( black tag )
And yes, I would think a little grease would be ok to use to hold things in place.