I was about to make just that suggestion. Use on/off buttons (rather than toggle switches) and latching relay circuits to control the valves.
There are mechanical latching relays, but I'm not talking about them. Take an ordinary normally-open relay where a spring keeps the contacts open unless current flows through the coil. Wire it with the contacts in parallel with the "on" button such that when push it, the relay closes and keeps itself on. Put a second button with normally closed contacts in series with the circuit so that when you push it, you interrupt the supply current and the relay drops out. That opens the contacts, so when you release the "off" button the relay stays de-energized and the contacts remain open.
Add indicator lights to show the state of the circuit. You might consider having both "on" and "off" lights, with the "off" light powered by the normally closed contacts of the relay.
Instead of finding a push button with normally closed contacts, you could instead use a toggle switch as your "off" control. Label it as "enable" when the contacts are closed and "off" when open. So now if you put the "enable" switch in the "disable" position, pushing the "on" button has no effect. Put the enable switch in the "enable" position and nothing happens until you push the "on" button again to activate the relay and open the valve. Turn the enable switch to "disable" and the relay opens and the valve closes, and again the "on" button has no effect.
Put your "emergency shut off" switch in series with the supply to all three relay circuits so that opening it shuts power off to them all. If you then close that switch again, the relays will remain off and the valves closed.
If you don't want to use electromechanical logic you could do this with logic circuits, but I recommend the old-fashioned stuff for its simplicity and ease of understanding, and also because it can be made to work at the oddball voltages required to control the valve -- "oddball" in the sense that they're probably different from logic levels, and you'd need level shifters and a drive transistor to control the valves with logic signals.
My high school electronics lab used exactly this mechanism to control the AC power to the lab benches. A set of ordinary wall switches, wired in series, were placed around the classroom as "emergency off" switches. Turn any one off, and the power dropped and stayed off even if the emergency switch was turned back on. The teacher had to momentarily activate a key switch on a panel to turn the power back on.