Looking at your system from the pics above. I'd say your better off calling an electrician than a plumber. Although not the way I would pipe it. It SHOULD work. I'd say there is a wiring problem. Probably between the zone valve, the pump, and the thermostat. Good Luck.
Every multi bay sink I have ever hooked up ( for a mechanical \ industrial use) has been to pipe in an indirect waste. You pipe all three sinks to either a mainline or individually and have them dump into a collection with a trap. That way traps on each are not necessary. It also allows you to...