Using a 28v source, is there a controller/switch that will run from the Arduino and do the 28 volt switching, preferable solid state? (There is the beefcake (KIT-1333815 ROHS), but mechanical relay making may be too audible to animals).
Is it easier to find a motor controller shield that will just replace the control circuitry and directly work this motor? And perchance a suggestion to which one?
Looks like the manufacturer is using a super simple SSR setup, and since you already have the pump opened up, you could just replace their circuit board with something the Arduino could drive directly, like a 5V triggered SSR to control 115V to the motor.