My calendar is a JLC with the IWC coordinated system. All I need (on the JLC adaptation) is a toothpick and a few flicks of the wrist. I imagine that this would be more burdensome if I actually had to adjust the indications separately and look up a moon age table online. The key is to not leave it unworn for so long that "correcting" the calendar becomes a marathon.
usually set the moonphase so I can see the moon. I rarely set the moon to a new moon. I figure I'd rather see the moon on the dial than be absolutely correct in its setting.
This is my Underwood safe shipped to me from Italy. The watches in the picture are not current as I have done a lot of changing but it certainly takes care of my perpetual and annual calendars!