1. The text says nothing about reorienting the timing of the 7th day Sabbath according to the moon phase.
2. The day of the new moon is not said to be a day of ceasing (Numbers 28:11-15). Only the 7th month's new moon day is said to be a day of ceasing (Numbers 29:1).
3. The Hebrew word for "week" (sh-b-ay, shvua) is consonantally identical (that is, same consonants) to the word for "seven" (sh-b-ay, sheva), linguistically implying a week as seven days. There is no mention of a week being less than seven days or longer than seven days. Instructions to count for seven full Sabbaths (Leviticus 23:15) does not imply anything regarding special weeks existing.
4. One feast which requires ceasing from work is already timed adjacent to the 7th day Sabbath (Leviticus 23:21), so attempting to create a calendar to avoid this is textually impossible. Saying that a feast day and a 7th day Sabbath should not fall back-to-back ignores this fact, because it already must in at least one instance per year.
5. The 7th day Sabbath is repeatedly stated to be on the 7th day of the week. There is no textual basis for shifting it or adding additional separate Sabbaths.
6. The cycle of the moon is not evenly divisible by 7, and the extra days required to adjust the calendar to make the lunar Sabbath theory "work" are never mentioned.
7. Ultimately, establishing the lunar Sabbath theory requires inferring a system based upon something that is NOT said rather than using any actual textual or linguistic basis. That is, it is based upon assumptions regarding completely unstated matters, and it requires the use of many new rules absent from mention in the text.
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It is certainly true that many other calendar theories have some similar problems. For example, use of the equinox is not referred to, nor is "sighting" the moon or the added rules to keep a repeatedly unsighted moon from causing significant deviation (i.e., "new month begins automatically after 30 days regardless of sighting"). In that sense, the aforementioned theories are not completely unique in going far beyond the text.
We can see, however, the connection between the "month" or "new moon" (ch-d-sh, chodesh) and "new" (ch-d-sh, chadash, or ch-d-sh-h, chadashah). We can also see the connection between a "week" (sh-b-ay, shavua) and "seven" (sh-b-ay, sheva). We can also see the alignment of the first month as being in conjunction with the ripening of the barley (Exodus 9:31, Exodus 13:4, Deuteronomy 16:1).
Therefore, I propose we recognize the day of the new moon as the day of the new month (instead of the day following the sighting of the new crescent), that we consistently recognize a week as seven days, and that we align the timing of the first month, the "month [of] the Abib", with the ripening of the barley. This, in my understanding and opinion, would not require the adding of unmentioned laws in order for it to be understood or to be done, and it would allow for the consistent alignment of the calendar with the seasons.
