If the system can't be made to have consistent flow demands, by either changing nozzles, or by combining low-flow zones to run simultaneously, then the old-school approach is probably beyond you. I would be looking hard and long at how the existing system might be altered to run from a standard pump, before I plunged the thousands into the more exotic pump.
The Cycle-Stop-Valve is a technologically simple solution to mismatched zones. It makes a pump match a low flow demand by running it at a high-pressure-low-flow point on its performance curve, and reducing that high pressure before the water reaches the ground-level plumbing and controls. Without question, the CSV works. Its one theoretical misgiving is that it creates high pressures on the upstream side of the CSV, which makes for some possible worry about how an old polyethylene drop pipe in the well will react to higher pressures. With a brand new pump install, the drop pipe can be Sch 80 PVC or even galvanized steel, should you so desire, and drop-pipe worries disappear.
If the system is very flawed in its design, then you may need a high pressure at the supply connection, and the pump/CSV combination might become a 1-1/2 HP pump and a deluxe brass-body CSV, with an output pressure above the 60 psi available from the plastic-body versions.
What you should be doing in the here and now, is what should have been done a very long time ago, and that is to get the booster pump back in operation with an extension cord, and to take pressure readings at the pump output for each zone of the sprinkler system.
Without some hard numbers for what pressures are at the sprinkler system connection point, it's a bit difficult to state accurately just what will and won't make it work again.
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Another possibility for a replacement for the current arrangement is a 1 HP submersible pump, along with a lower-power booster for certain zones of the system. That combination might be operable from the same wiring that powers the existing pump.