I've been studying what happed to the Torah after AD70, by decree of rabbis dealing with loss of the Temple. Very interesting, and time consuming. The Torah had it that ALL men of Israel had to show up at Jerusalem for Passover, Sukkot, and Shavuot. That required three pilgrimmage to Jerusalem, leaving border defences unguarded, though God promised would not be a problem. The caveat in that was the effect of Roman dispersions of Jews in the latter years of nation Israel. Many were simply relocated too far away for three trips to Jerusalem Along the way the requirement was changed to first born males for the sake of economy, and many Jews having been dispersed too far away. Each would have to deal with travel time by foot or animal, plus the weeks in Jerusalem. The logistics of all that outstripped the Torah expectations. I'm currently tracking that to the modern essentially "not at all" mode, except for the mode of tourism during those and other holy days per choice of attendee, male or female.
The fact that any Jew was required to make any sacrifice even occasionally carried the fact it was necessary to repeat sacrifices for sin. One could not cover all sins by sacrificing once, once a year, once a decade, once for all. That's the basis of the benefits of sacrifice of animal blood to last only year to year by repeated observances. The problem you raise about priests bridging years of uncovered sins shows additional perversion of Torah. The problem was accommodation of Jews needing a break.
The Exodus Passover observances didn't solve Israel's sin problem. It took JESUS to fix that.
If you study it onward, I welcome you to teach me the gaps in the above statement. I really do lack time to carry it much further.
Meanwhile I submit
Acts 13:29-41 (KJV)
29 And when they had fulfilled all that was written of him, they took him down from the tree, and laid him in a sepulchre.
30 But God raised him from the dead:
31 And he was seen many days of them which came up with him from Galilee to Jerusalem, who are his witnesses unto the people.
32 And we declare unto you glad tidings, how that the promise which was made unto the fathers,
33 God hath fulfilled the same unto us their children, in that he hath raised up Jesus again; as it is also written in the second psalm, Thou art my Son, this day have I begotten thee.
34 And as concerning that he raised him up from the dead, now no more to return to corruption, he said on this wise, I will give you the sure mercies of David.
35 Wherefore he saith also in another psalm, Thou shalt not suffer thine Holy One to see corruption.
36 For David, after he had served his own generation by the will of God, fell on sleep, and was laid unto his fathers, and saw corruption:
37 But he, whom God raised again, saw no corruption.
38 Be it known unto you therefore, men and brethren, that through this man is preached unto you the forgiveness of sins:
39 And by him all that believe are justified from all things, from which ye
could not be justified by the law of Moses.
40 Beware therefore, lest that come upon you, which is spoken of in the prophets;
41 Behold, ye despisers, and wonder, and perish: for I work a work in your days, a work which ye shall in no wise believe, though a man declare it unto you.
Christians are decaring that upon you!