I believe your problem is associated with the water inlet lines to the pump. Notice how you will need to pull (suck) a lot of air (bubbles) downhill against a water column on the inlet lines to your pump.
First, redress the inlet water lines to minimize the down hill flow as much as possible. Then when priming the pump on first start open as many water taps as possible to increase the water flow through the pump which will, if you get it right, rid the inlet lines of air pockets.
IMO, it is the bubbles of air going through your pump that makes it sound like a machine gun. To prove or disprove my theory of the noise source see if you can manually fill the pump inlet water lines with water, then connect to FWT and test same for noise. JMO.