The secret incantation for zeroing is "G92 Z0". when sent from pronterface this saves the current z position as the 0 point. so once you have it at the right height using the 0.1mm up/down buttons, just send the magic words. if the correct position is lower than the current 0 point, you may will first have to do "G92 Z10" in order to let it move lower.
Once you get it dialed in, i think it needs to get written into eeprom to avoid losing the setting after a power cycle. i'm not sure if there's a command for that or whether you will need to reflash the controller.