Just closing the valve to the house will probably cause it to start building pressure again. As a short term you can partially close the ball valve to throttle flow and it will function(poorly)
The Burks pump was a deep well jet pump it had a regulator built in, its what the bolt sticking out the top was for. Your new pump is a convertible jet, they can be set as up as either a shallow well jet or a deep well jet. You need to add the regulator separately.
Everything is dependent on the actual water level, if the water level is up high it doesn't take much pressure to force water through the jet and it can do fine without a regulator. The further down the water is the more back pressure the pump needs to force water down through the jet. Without a regulator if you draw more water than the pump can produce it drops the pressure to zero leaving no pressure for the jet. A regulator throttles the water to the house maintaining sufficient back pressure for the jet to operate.