Here's an interesting page i found when searching on "dead sea scrolls". The link is:
It gives different Sabbath dates for specific months, maybe even for 1 specific year, and makes reference to the elusive "364-day year". I make no claim pro or con. Text follows:
Paraphrase and comments by Kirsty Antosy
4Q327 is part of the scrolls known as the calendars. In the calendars, the festivals of the year and the rituals are determined, using priestly rosters. The manuscripts were found in very bad condition. They were also found with several other fragments making it difficult to determine what the remains actually were. Because 4Q327 is in the same handwriting as one manuscript of A Sectarian Manifesto, it is sometimes argued that it should be considered part of that document. Abegg argues against this on the basis of the structure of the latter document. (Wise, Abegg, & Cook, p 319)
4Q394 was found in Cave 4 manuscripts. 4Q394 is part of the Halakhic Letter. The Halakhic letter is very important, for it outlines the rules and rituals found in a particular interpretation of the Old Testament. The rest of the works were lost, leaving it unfeasible to determine the true meaning of the Halakhic Letter. (Martinez, p 77) Some believe that it was composed as a way to contrast the Qumran group from the rest of Judaism. Each line of the composite text is numbered consequently, for easier reference to the fragments, which have been preserved.
4Qcalendrical Document (4Q327)
Frag. 1 col. I
The sixteenth of the month is a Sabbath. On the twenty-third of the month is a Sabbath. On the thirtieth is a Sabbath.
Frag. 2 col. II
On the twenty-first of the month is a Sabbath. On the twenty- second is the feast of oil. There is an offering after the Sabbath. On the twenty-eight of the month is a Sabbath. The month continues with Sunday the day after the Sabbath, Monday the second day after the Sabbath, and an additional day, Tuesday.
Frag. 2 col. III
On the fourth of the month is a Sabbath. On the eleventh of the month is a Sabbath. On the eighteenth of the month is a Sabbath. On the twenty-fifth of the month is a Sabbath. The second of the fifth month is a Sabbath. On the third of the month is the festival of wine.
4Qhalakhic Letter (4Q394 [4QMMTa])
After the Sabbath, there are three days added and then the year is complete, three hundred and sixty-four days. There are some rules concerning God, which are part of the works we are looking at and they all relate to the purity laws. When wheat is offered, Gentiles cannot touch it. No one should accept wheat from the Gentiles. No wheat touched by the Gentiles will be allowed in the temple.
The flesh of the scarifies should be cooked in bronze canisters. Both the meat and the broth of the sacrifices should be taken outside into the courtyard. The sacrifice is of the Gentiles, what we think is a sacrifice is an offering of thanks, which is postponed from one day to the next. Concerning this sacrifice, it should be a man of stature who has a woman with him.
The cereal should be eaten with the fats and the meat on the day of sacrifice. Sons of priests shall oversee this meal so that the sons of Aaron do not lead the people to sin or bother them with it. The priests shall oversee the purity of the red calf, so that all purity laws are followed. Whoever slaughters, burns, collects and sprinkles the ash does so by the purity rituals. This should all be completed by sunset, so that those who have sinned can be forgiven for their sins. This shall be done for the sons.
 This is the calendar of the feasts for the second month (WAC 319).
 This is the calendar of the feasts for the third month (WAC 319).
 One of the extra-biblical feasts found among the Dead Sea Scroll calendar texts (WAC 319).
 This is the calendar of the feasts for the fourth-fifth month (WAC 319).
 The year is complete after 364 days.
 Assumed to be the sons of Aaron
Martinez, Florentino. The Dead Sea Scrolls Translated. New York: 1996
Vermes, Geza. The Complete Dead Sea Scrolls in English. 1997
Wise, Abegg and Cook. The Dead Sea Scrolls: A New Translation. 1996
prepared for Intro. to the Hebrew Bible
by Kirsty Antosy