The sabbath was never determined by the lunar cycle. Month in Hebrew is chodesh (related to the word "new" because of the new moon) and Yerach (which also means "moon". The word for week is Shavu'a, related to sheva, seven. The word for day is Yom which refers to the daylight period (check the earlier Syriac) as opposed to the dark period. The day is the cycle of light and dark as fixed by the cycle of the sun. The word mo'ed (which your article references) relates to seasons and holidays (which are mostly lunar with a little solar mixed in), not the sabbath cycle.
In ancient Jewish life, the day did not change -- it was always the seventh day as counted from the previous sabbath. The references to the day of the month in the bible were for holidays, not for the sabbath.