First, I need to understand where you placed the full-wave rectifier. I assume you added it between COM and say station 1? If would be best if you can provide a sketch. Note that you should not replace the half-wave recfitier (used for 24VAC to 5VDC conversion) on the OSPi with a full-wave rectifier — this is because the control mechanism of OSPi requires a half-wave rectifier, if you replace that with full-wave rectifier, it is not going to work.
Second, it’s possible to directly replace a triac with an NPN transistor. The triac’s G, MT1, MT2 pins are functionally equivalent to an NPN transistor’s B, E, C pins. If you intend to only replace 1 triac with transistor, you may consider making use of the built-in relay instead (the relay is rated 250VAC/3A, however, I recommend only using the relay for low voltages, such as below 40V, because the PCB traces and the enclosure are not rated 250VAC).
Lastly, a question: what type of pump relay do you have? A lot of sprinkler pump relays operate on 24VAC, so I am not sure how you can get them to work by converting 24VAC to DC.