Alas, the common wire is actually interconnected with 24+ voltage, your controller “grounds” the zone output to 24- voltage when it should be active.
One option to consider is to drive two of the zones with a wire splitter. These work by encoding information on which output should be active and allowing two zones to share a single wire (thereby freeing one extra wire). Flow meter will not work on these, but moving your zones to it and hooking up the water meter to the two free wires should work.
More on these splitters here: