MIC5216 Achieve minimum quiescent current draw
Is there a way, to reduce the power on the enable pin to 0.18V while
  the 328p is asleep without completely pulling that particular pin low
  and as soon as an interrupt is triggered to wake the whole circuit up
  again?


At 0.4V and below the regulator is turned off, so the 328p won't just be 'asleep', it will be dead, and the only way to make it 'wake up' again will be to turn the regulator back on via an external circuit. To do this you could make the pushbutton pull the Enable input high when pressed. On startup the MCU would also pull the Enable input high to keep the power on, and let it go low to power off. If you need to remember the program state while the MCU is off it could save the required info in the EEPROM just before powering down (remembering to give it time to write the data!)     

If the MCU must stay powered all the time then to get lower sleep current you will need a different regulator. The MCP1703 should do it if peak current doesn't exceed 200mA. However you are powering a servo which which might need more than this.