Parsha Chabura AchareiMos/K'doshim: Avoda of Kohein Gadol on Yom Kippur

This weeks chaburah discussed the role of the kohein gadol on Yom Kippur. The gemara in Yevamos (33a) learns from a g'zeiras hakasuv that the kohein gadol had to do the avoda on Yom Kippur. The question is, exactly which avoda is this referring to.

Shittas Ba'al Hamaor

The mishnayos in Perek 2 of Yoma discuss the four lotteries that were held everyday in the Beis HaMikdash. The Ba'al Hamaor in the beginning of Yoma asks why was it necessary to hold a lottery on Yom Kippur if the kohein gadol did all the avoda. He answers ain hachi nami there was no lottery on Yom Kippur.
Tosfos (20b) also quotes a shitta like this and brings the following rayah. The terumas hadeshen wasnormally done at alos hashachar. On Yom Kippur it was done at midnight due to the weakness of the kohein gadol. Tosafos writes that they didn't want to overtax the kohein gadol so they had a kohein hedyot do the terumas hadeshen and since a kohein hedyot couldn't do any avoda on Yom Kippur, they had to do it at midnight.

Shittas Ramban/Rambam

The Milchamos argues and says that the machshirei avoda was done by a kohein hedyot. The lotteries were to decide which kohanim got to do the machshirei avoda (ayin Tosfos Yom Tov 2:2 for a synopsis of the Ramban). Furthermore, the terumas hadeshen is an avodas liela and could be done by a kohein hedyot. They did it at midnight to give the kohein gadol more time to do the rest of the avoda on Yom Kippur.
The Rambam seems to agree with this but is mashma that there were only two lotteries not four (ayin avodsas yom kippur 4:1)

Shittas Ritva Yoma 12B

The Ritva says m'd'oreisa there was a chiyuv for the kohein gadol to do the special yom kippur avoda. It was only a mitzva for the kohein gadol to do the rest of the avoda which would have taken place even during the week (korbon tamid). However, Chazal created a chiyuv d'rabanan on the rest of the avoda but this chiyuv did not extend to the machshirei avoda.

He'oros/Nafka Mina

1) The Sha'ar HaMelech (Avodas Yom Kippur 1:1) has a long discussion whether a kohein hedyot who does the avoda on Yom kippur is chayav misa. Since he is considered a "zar" maybe this state of "zarus" creates a chiyuv misa (also see D'var Avraham Siman 23:14).
One could argue that according to the Ritva this kasha only applies to the avoda specifically done on Yom Kippur. For the other avoda even if it is a mitzva for teh kohein gadol to do it, a kohein hedyot could still do it and not be chayav misa.

2) The Chiddushei R' Aryeh Leib discusses the nature of kiddush yadayim v'raglayim on Yom Kippur. He writes that in actuality as long as you do one kiddush at the start of the day, the rest of the avoda isn't pasul even though you really need to do 10 kiddushins. However, the kiddush done for the treumas hadeshen (assuming the kohein gadol did it) would not work cause you need a kiddush yadyaim that was done for the Yom Kippur specific avoda-this is in line with the Ritva who he actually quotes.

3) I am not sure if the Ohr Sameach (Avodas Yom Kippur 4:1) agrees with this Ritva. The Ohr Sameach writes that when Yom Kippur falls on Shabbos, the musaf for Shabbos must be brought by the kohein gadol. The reason is that all the korbonos of that day get the status of a "Yom Kippur" korbon even if the reason they are brought is not because of Yom Kippur. This would imply that even the non Yom Kippur specific-avoda must be done by the kohein gadol and it is not just a mitzvah for the kohein gadol to do it.