Are these multiple zone valves wired from controller to zone valve(s) with no field splices? If you only had a few of them, or even more than a few, you could duplicate the pump start workaround for each 3-valve zone. Because of home automation controls, relays that plug into sockets with screw terminals are available for cheap. From a cost standpoint, a bank of workaround relays added to a 22-zone Rainbird ESP-Me might get you home for under $500 (but spend the extra benjamin or two for something a bit more robust.
Available in 10-packs at a unit price of less than $5.00