I think it sounds like a not balanced pump axle, or a defect pump unit. Can you strip the pump and take a look at the axle and in the inner side of the pump?
I am not sure if this pump has a bearing for the axle but this could be false connectet to the case?
Do you think it could be the pump when it sounds good "solo" not connected to the system? Maybe the pump starts to sound like this when it need to use more power connected to the system? (suction). I can try open it and check.