Thanks to Chatzkel, Avrohom Yitzchok and Double AA, the following sources were found to be helpful.
Rambam, Mishneh Torah, Hilchos Avodas Yom HaKippurim:
The order of all the practices carried out on this day is the
following: At midnight, the lottery is held for the removal of the
ashes of the altar. The wood for the altar is arranged and the ashes
are removed from the altar as is done each day according to the order
we explained until they reach the slaughter of the continuous
offering. When they reach the slaughter of the continuous offering, a
linen sheet is spread out between the High Priest and the people.
Machzor Yom Kippur Ashkenaz; Musaf Yom Kippur, Seder Avodah
a week before the tenth day [of Tishrei], secluded the High Priest as was done in the seven days after the completion of the Mishkan. They sprinkled upon him water mixed with the ashes of red heifers in order to purify him.
Avodas Hakorbanos by Rav Aharon ben Rav Yosef HaKohen (ArtScroll).
It includes a section on Avodas Yom HaKippurim. The blurb writes:
Written by the Chafetz Chaim's son-in-law, Rav Aharon ben Rav Yosef HaKohen, Sefer Avodas HaKorbanos offers a clear exposition of the avodah in the Beis HaMikdash, including all the karbanos (offerings). This classic is available for the first time with an elucidated English translation, including a brief explanatory introduction to each paragraph, notes and diagrams that make the beauty of the Beis HaMikdash services accessible to all of us.
Also includes fascinating and detailed section on Avodas Yom Kippur.
The Korban Chatas by Rabbi Menachem Oppen (Feldheim)
The blurb writes:
If you have not been fortunate enough to walk your own sheep or goat to the Bais Hamikdash, to recite viduy on its head and watch it be slaughtered and burnt in your stead, to feel freed of the burden of sin, you will be relieved to know that kaparah can also be attained by delving into the Parsha of the Korban Chatas.
This groundbreaking volume, The Korban Chatas, will guide you through
the entire process, illuminating the many halachos passuk-by-passuk
with lucid explanations, engaging illustrations and comprehensive
footnotes. Elusive animal parts are identified in detailed diagrams
and photos. The Korban Chatas will come alive as you gain a vivid
understanding of this most central avodah from start to finish.
The clear and concrete learning derived from this sefer makes it an
invaluable aid for the Rebbi and talmid, a treasure for scholars, and
a delight for every soul yearning for the Bais Hamikdash and its
ultimate purpose of kaparah.