Raising pressure with pump?

[LLigetfa]

You could also put a low pressure cut off on the suction side of the jet pump.

That should work but I would advise to use a reverse pressure switch, not a conventional switch with low-cutoff as they need to be manually reset when they trip.

Also, I would use it in conjunction with a CSV so that the pump doesn't run at max GPM while refilling the pressure tank. If the pump is let to run flat out, it will not only pump as much as is being drawn but will also see the pressure tank as additional draw.

Many folks don't quite understand that low pressure is often a side effect of low flow so trying to increase the flow will lower the pressure on the pump inlet to below zero. In the OP's case with the leak, much of the flow is robbed by the leak so it really is a flow problem, presenting as a pressure problem.

 

[Valveman]

For a low suction safety switch you really need one that is manually reset. A reverse acting switch on the suction side will shut the pump off when the suction pressure is low. As soon as the pump shuts off the inlet pressure increases and the switch makes the pump start again. This can cause a lot of quick cycles that are not good for the pump or anything. When a pump goes off on low suction pressure from a pressurized source, it is best to have a pressure switch that won't keep resetting itself over and over.