I'll jump in here and share some of what I have found on this. And then we could all discuss it.
1. All the feast days in the old sanctuary system were scheduled from the new moon of the first month of the sacred year, (the beginning of which was corresponding to the last of March and the beginning of April. PP . 537.)
Whenever the new moon, used to designate the timing of the feast days, (which would be the first and the seventh new moon, beginning the first and the seventh month of the sacred year), falls on a seventh-day Sabbath, then all the shadowy Sabbaths (ceremonial Sabbaths) which are calculated from that new moon, also, fall on seventh-day-Sabbaths KJV. This is God's mysterious code. It was this prophetic code that Jesus revealed to His disciples 2000 years ago, which was later lost during the dark ages, and is only now being rediscovered by God's people today.
2.This is apparently the reason God links these two significant days together, the seventh-day Sabbath and the new moon, in the new heaven and the new earth which He will create. In combination, they are the key, that unlocks the prophecies of Moses, as revealed in the old covenant system of Hebrew worship. (Isaiah 66:22-24.)
"For as the new heavens and the new earth, which I will make, shall remain before me, saith the LORD, so shall your seed and your name remain. 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 the LORD. And they shall go forth, and look upon the carcases of the men that have transgressed against me: for their worm shall not die, neither shall their fire be quenched; and they shall be an abhorring unto all flesh." Isaiah 66:22-24.
"And there appeared a great wonder in heaven; a woman clothed with the sun, and the moon under her feet, and upon her head a crown of twelve stars:" Rev. 12:1 KJV.
3.The spring feast days from Passover to Pentecost number 52 days, according to the Bible evidence (Leviticus 23:5-16, 1 Corinthians 15:4 KJV), and the main Hebrew calendars in use today. (There is no variation in the count of the days, or the manner of observance from year to year) The ceremonies within the spring feast days were observed unvaried every year, this indicates that there was no specially designated year, when these spring feast days would meet their fulfillment from the books of Moses. (The prophet Daniel, however, in Daniel 9:27 says it was to occur in the midst of the 70th week of years.) This, however, was not the case for the fall feast days.
4.Unlike the spring feasts, the fall feast days, 22 literal days, had extra special ceremonies that where performed only in the Sabbatical and Jubilee years, clearly, indicating that their main fulfillment would be in these two special years.Some of the fall feast days had extra special ceremonies in the Sabbatical year only(the year of release). The law of God was read to all, men, women, children, and the stranger during the days of the Feast of Tabernacles (Deuteronomy 31:10-16). This practice was reserved just for the Sabbatical year(the year of release).
Deuteronomy 31:10-13 KJV "And Moses commanded them, saying, At the end of [every] seven years, in the solemnity of the year of release, in the feast of tabernacles, When all Israel is come to appear before the LORD thy God in the place which he shall choose, thou shalt read this law before all Israel in their hearing. Gather the people together, men, and women, and children, and thy stranger that [is] within thy gates, that they may hear, and that they may learn, and fear the LORD your God, and observe to do all the words of this law: And [that] their children, which have not known [any thing], may hear, and learn to fear the LORD your God, as long as ye live in the land whither ye go over Jordan to possess it.)
5.The Day of Atonement also, had extra special significance in the Sabbatical year(year of release), when certain classes of Hebrew slaves were set free (Deuteronomy 15:1, 12). This evidence shows that a fulfillment of the Day of Atonement can be expected to take place in a Sabbath year. No doubt, this is the Sabbatical year that precedes the year of Jubilee.
The reason for this is that there are 4 shadowy Sabbaths that must all come on seventh-day Sabbaths in their fulfillment, and this always happens in two consecutive years, Remember the year before the Jubilee year is always a Sabbatical year.
6. There is only one feast day that had extra special significance, in both, the Sabbatical year and in the year of Jubilee, and that fall feast day is the Day of Atonement. In the Sabbatical year a certain class of Hebrew slaves were set free (Deuteronomy 15:1, 12. PP 532).
The Day of Atonement has special significancein its fulfillment in the Sabbatical year, but its prime fulfillment was reserved for the commencement of the Jubilee (Leviticus. 25:8-10).
7.All other slaves waited for the Jubilee trumpet to sound on the Day of Atonement of the Jubilee year (Leviticus. 25:9,10, PP 534). The Jubilee trumpet was blown only on that special Holy day, when all slaves where set free from slavery. ( So it can now be clearly seen that Jesus designed the Day of Atonement to come on the tenth day of the month, because only then, are all four of the shadowy Sabbaths within the fall feast days, positioned to come on seventh-day Sabbaths in these two consecutive years, the very years when they have their extra special significance. Isn't that amazing!