Should the New Moons be kept as Sabbaths?

Yes, or you would end up with a work week that exceeded six working days. According to the Universal Jewish Encyclopedia:

The New Moon is still, and the Sabbath originally was, dependent upon the lunar cycle . . . Originally the New Moon was celebrated in the same way as the Sabbath; gradually it became less important while the Sabbath became more and more a day of religion and humanity, of religious meditation and instruction, of peace and delight of the soul (p. 410)

The New Moons were linked with Sabbaths as a special class of holy days. They were days of rejoicing and feasting with even more sacrifices preformed on New Moon then were offered on the seventh-day Sabbath. Like the seventh-day Sabbath, the New Moons were to be days of rest with no buying and selling. (See Amos 8:5.) Those who keep the seventh-day Sabbath have long used Isaiah 66:23 as proof that the seventh-day Sabbath will still be kept throughout eternity: "And it shall come to pass, that from one new moon to another, and from one Sabbath to another, shall all flesh come to worship before me, saith Yahuwah."

The question is then asked, "If we're going to be keeping the seventh-day Sabbath throughout eternity, shouldn't we be keeping it now?" This text reveals that the calendar by which we will be keeping the seventh-day Sabbath is one on which the New Moons are also observed as worship days. If we will come to worship Yahuwah on New Moons throughout eternity, should we not come to worship Him on those special days now as well?