[Mark McLeod]

The compressor doesn't pull it's power from the control board. It pulls it from the 12V battery source through a spike relay.
The controller only serves to switch the spike on/off based on the pressure switch and actually stays out of the main current flow.

Try thinking of it as two separate circuits you are building:
1) A 12v circuit connects a 12V DC source through a spike (and a circuit breaker or fuse) to the compressor and also through spikes (and breakers) to power the solenoid valves. The control board will also need to be supplied power just to run.
2) A separate control circuit overlays this with the control board sending control PWM cables to each of the spikes.

Take a dorm room overhead light as an analogy. The control circuit is the "finger" that flips on the spike "light switch" allowing the house power (your 12V) to flow to the overhead light (your compressor).

In your case run the compressor to reach your operating pressure using the pressure switch, and use different limiting switches to control the solenoid values inflating/deflating the bladder.