First, help us understand what you have.
You mention a jet pump. Do you have a shallow well jet pump (one pipe to the well) or a deep well jet pump (two pipes to the well)?
What is the diameter of the casing of your well? Is it a drilled well (3' to 6" casing) or a dug well ( 2 to 3 ft casing)?
How deep is it to water in your well?
Do you have any idea how much water the well can produce (Not the size of the pump now)?
Is cost a significant consideration?
Are you planning to do it yourself or hire someone?
I would not go with the constant pressure sustem with a 4.5 GPM pump. It is barely going to make the flow you need, so you need a storage tank.
A 1 HP pump seems large for 4.5 GPM. If you get a submersible you will probably be able to use a pump with less horsepower than a jet.
The loss of pressure could be a leaking foot valve, which is a check valve at the bottom of the pipe going into the well. It is possible that you could work around that by installing a check valve at the inlet of the pump, though there are reasons not to do that.