Is there a way to have the pump relay turn on only for specific zones

Alas zones are driven with an AC power, meaning that the diode would act as a halfwave rectifier, whereas supply to the singular 24V relay would be OFF for 50% of the time

It is possible to add a sizable capacitor and drive a DC relay, such as what is described by @Stewart here:

But the downside of such approach is that, as far as the current draw, Rachio would see 3x the load during the one half cycle (1x zone solenoid + 1x DC relay + 1x capacitor charge), compared to another (1x zone solenoid). Depending on the relay, and inefficiencies of the components involved (diode, current limiting resistor, capacitor, etc…) you may run into the limits of the supply and the current limit protections.

There are improvements to the idea which can be implemented, such as using a smaller capacitor and driving the triac driver to run an AC relay full term, but at this point there are better, and cheaper, solutions which were discussed.