I'm just curious what pressure loss and flow the system was designed for? 40 lbs at the tank seems normal but it would be impossible to know if it will create enough flow without knowing what other components contribute to the total loss: the pipes, the valves, the sprinkler heads themselves. How much flow do you actually need? The general rule of thumb is 20GPM @ 40-50PSI per acre. How much are you trying to cover? How deep is the well, by the way and is there any elevation change between the sprinklers? Different sprinklers respond differently to pressure, which exact part numbers are your pop up heads and those you call "large"?
Anyhow, I just wanted to point out that properly designing a well pump-fed irrigation system takes quite a bit of calculations and you should get all your data in order and do some calculations before trying to balance it all empirically.
Lookup all your pump, sprinklers', valves', filters' etc. pressure and flow data, measure the length of all pipes, write down diameters of mainline and laterals. Measure elevation drops if any. Then draw all your components on the schematics and get your calculator handy. This is a slower way to troubleshoot but it's the only sure one.
The calculations formulas are in most of those user manuals and if you've discarded those, are available online. If you like, you can post your data here and I will check it, too.