How about just picking a non-cyclical time? Just count the amount of seconds/milliseconds since 1 Jan 1970 where the duration of the second is synced to those o

How about just picking a non-cyclical time? Just count the amount of seconds/milliseconds since 1 Jan 1970 where the duration of the second is synced to those on earth. Just have no official days/hours/years whatever, no leap seconds, no adjustments, no nothing. Those details can be filled in at will by whoever needs lunar time for daily use.