Connect C wire for nest thermostat on a zoned HVAC system
Connect a spare wire from the thermostat to the M1 terminal for that thermostat's zone
The wiring diagram posted for your zone board specifies that thermostat C wires should be connected to the M1 wires for their corresponding zones, along with the return from the zone damper motor.  So, I'd take a spare wire (black maybe? or purple/blue) from the cable from the thermostat and connect it to the corresponding M1 terminal (far right terminal in the zone block) on your zone board, then hook up your Nest, turn everything back on, and enjoy!