The problem you are having is water hammer most likely caused by a bad checkvalve in the pump. It would be good to know if there are more checkvalves in-line in the drop pipe or at the wellhead. When the one in the pump goes, the others quickly follow like dominoes. I didn't see one at the tank in the video. When the pressure switch kicks on, is there any delay before it flows?
In my home I deliberately strapped my poly pipe to the underside of the floor joists so that I can hear when the water flows. My thoughts at the time was that if it was too loud, that I would replace the metal pipe strapping with rubber to isolate it but didn't find the noise to be too bad.