The pressure drop in both the suction and pressure side indicates a problem with the pump itself and for some reason the pump is not pumping as much water during this period. This could be caused by several things but since you replaced so many parts, I suspect it is a lot air entering into the pump chamber.

The lid gasket can go bad so the pump lid does not seal. But if that happens, you should see air in the pump basket. Also there can be cracks in the lid or even the pump housing which can draw in air into the pump. This can be due to a lot of air entering the pump. If that is happening, then the filter should fill up with air and you should see air coming out of the returns. Most of the time if there is a crack in the pump housing it is on the pressure side so you can easily see water leaking out but if it is on the suction side, it will be harder to detect. Does the pump leak any water when it is off? Also, when you used the shaving cream did you put any on the front half of pump housing?