I don't know if you have a pressure issue, as much as a flow issue.
Do you know what the output (GPM) of the jet pump was? And the combined output of your sprinkler heads?
It sounds to me like you might just need to downsize the nozzles of your zones, or increase the size of your pump and suction line.
Without knowing what "sprinkler" pump you have, you might have a booster pump, which is not designed for suction per say.
What kind of "Tubing" are you using for your suction line?