The code for the Kegboard Pro Mini could probably be modified to control relays on GP2 and GP3 to control solenoids. But that will only be able to control 2 taps per KBPM. You'd need to 2x KBPMs and a USB hub to connect it all together. Along with the difficulty of acquiring KBPMs, you may be better off going the Arduino route.
I've not tried to use an Arduino since I have a couple KBPMs, but the specs look the same on the Micro as the Leonardo (the KBPM equivalent). What issues are you having compiling?
Looking at kegboard_config.h it looks like you'd need a Arduino Mega to support up to 4 taps.
I've see a few posts about people using solenoids and recommendations for them here on the forum. search around.