Hello anymouse,
didn't God work for 6 days and rest on the sabbath? and isn't a fast a rest? I don't really see the problem with having to break your fast on the Sabbath for "religious reasons".
BTW. You are not on an "Atkins Diet" when fasting, as your body is feeding from protein on Atkins, but while fasting you are basically living from fat stores. Ketosis means a stage in fat-metabolism which is stimulated primarily when the liver is low on glycogen or stored glucose.
Breaking the fast at 7 day intervals will only interrupt ketosis, restart digestion, and delay the healing and cleansing, which are the primary reasons in fasting for health.