Ok, I am starting to run out of ideas but I am not willing to give up yet. If you have a suction gauge, it might be helpful to find out what is happening on the suction side of the pump during this period of pressure drop. If the suction increases during this period, it could be cavitation that we are hearing and then we just need to figure out what is causing the suction to increase. If the suction decreases, it could mean that there is something occurring inside the pump besides cavitation. Most gauges with 1/4" fitting will fit the suction side drain plug.

If you want to give up, I completely understand. These types of problems can be very frustrating.