Rabbi Prof. Yoel Elitzur wrote in his book "Makom Ba'Parasha", pg. 425 (my translation):
"First of all, we must remember that Yerushalayim was only chosen in the time of David and Shlomo. Prior to that, the Tabernacle was in different places, but the mitzva of the work of Yom Kippur always existed. Meaning, "Azazel in the desert", ...
The Mechaber in Shulchan Aruch 607:4
עונות שהתודה עליהם ביום הכפורים שעבר ולא שינה עליהם אפ"ה יכול לחזור ולהתודות עלי:4
Regarding sins for which one confessed on the previous Yom Kippur and did not repeat, he may confess them again.
The Mishna Berura in 607:13,14
אפ"ה יכול וכו' - אף בין אדם לחבירו גנב וגזל וכדומה אע"פ שמחל לו והשיב את ...
This is an interesting question for sure! Although I did not find anything that discusses the issue on it's own, I do have a few points that can possibly answer your questions mentioned.
Firstly, there is a מחלוקת if the כ"ג can even die in the ק"ק or only in the היכל. Here is the מהרש"א Yoma 19B in חידושי אגדות
רגל עגל כו'. כתב הריטב"א ...