M.J. ...There are several different issues involved here, such as how early the calendar itself was known, when it was actually put into practice as opposed to utilized theoretically in literature, and sort of status it had when it was put into practice. Some, such as Rachel Elior, have claimed that the solar calendar goes back to the pre-exilic period (assuming continuity in Zadokite cultus on both sides of the exile), but this is quite unlikely since the sources that seem to betray it are comparatively late (e.g. the Priestly material in the Pentateuch instead of D or JE, 1-2 Chronicles instead of 1-2 Samuel and 1-2 Kings, etc.). There is much dispute and uncertainty about when it came into use and its status in the Persian period because sources are so scarce. Annie Jaubert claimed that the calendar was the official cultic calendar as early as the first centuries after the Exile, VanderKam more cautiously admits that the evidence is "elusive" as to whether it had official status so early even if it was used early in priestly texts, while most agree that it was in use liturgically by the Maccabean period; Hanan Eshel in particular believes that the solar calendar was generally accepted by Jerusalem priests only since the third century BC.
The main finding is that the calendar had cultic importance beyond Qumran Judaism (e.g. in the pre-Maccabean priesthood), tho by the mid-second century BC it survived only among the Essenes and probably the Samaritans. Traces however can still be found in the liturgical calendar of the Sadducees who followed the Zadokites in conducting the Jerusalem priesthood; their reckoning of the festival of Shavuot, in contrast to the Pharisees and later rabbis, was done in the same way as in the solar calendar of the Jubilees and 1 Enoch, for instance. That Daniel follows the same understanding of monthly reckoning as 1 Enoch is not surprising considering the otherwise close kinship between the apocalypses of Daniel (which has overarching priestly concerns, cf. especially ch. 8-9) and 1 Enoch.
BTW, it should not be misunderstood that the public calendar was not lunisolar (with lunar monthly reckoning) throughout the period. It is generally recognized that the solar calendar, used to set the priestly duties and festivals, co-existed with the lunisolar calendar and both may have even shared the same weekly reckoning of the sabbath; they differed in how the weeks align with the months and whether the festivals fall on the same day of the week year to year. Hence, the extensive efforts in the Qumran calendrical texts to synchronize the two calendars.