If you have 24 PSI, then your spring is 55’ in elevation, so good guess. Most modern appliances these days need about 50 PSI. I don’t see that the galve tank is doing you any good. If there is no air in that tank, it is just like a large piece of pipe in the line. A cup of water has to go into that tank, before a cup of water will come out. So it is not doing any good as storage. The bladder tank could give you a little storage if the air charge is set at about 10 PSI. But there needs to be a check valve before the bladder tank or it will push water the other way when the line from the spring is dry.
If the water supply is steady, all you need is to boost the pressure from 24 to 50 PSI. A ½ HP jet pump with a 40/60 pressure switch placed before the check valve and bladder tank could do that. A Cycle Stop Valve would keep the pump from cycling on and off excessively, and allow you to use a very small bladder tank, or work with the one you already have.
If you continue to gravity feed the irrigation and use the pump for the house only, it won’t use 2 dollars of electricity a month.
Here are a couple of pictures of a Jet pump with our new Stainless Steel Cycle Stop Valve, and the second one has our new electronic pressure switch.