Question: The Beraisa teaches that Hagralah is a Mitzvah which is not Me'akev?!

This fits nicely according to the first Lashon.

According to the second Lashon, however, there is an opinion which maintains that Hagralah is Me'akev!?

Answer: The Beraisa is correctly taught that Hanachah is a Mitzvah.

The Beraisa teaches that it is a Mitzvah to do both Goral and Vidui, but that neither are Me'akev, and here the Goral cannot mean Hanachah!?

R. Shimon disagrees and holds that Vidui is Me'akev.

This reading implies that R. Shimon concurs that the Goral is not Me'akev.

Question: If the Goral here means Hanachah, then R. Shimon would hold that our Goral (Aliyah) is Me'akev (Yet, R. Shimon holds that it is not Me'akev as we see from the case where one of the Se'irim died)?!

Answer: R. Shimon was unsure of the position of the Rabanan and taught his position that both Hagralah and Vidui are Me'akev regardless of what the Rabanan mean by Hagralah.

We see the positions of R. Shimon and R. Yehudah as two alternate explanations for the Beraisa regarding the order of the Par and Sa'ir.

The Beraisa teaches that preempting the Par with Avodah of the Sa'ir is Me'akev that Sa'ir, but the reverse is not.

What is being referred to as the Par before the Sa'ir?

It cannot be the Matanos of the Par in the Heichal before the Matanos bi'F'nim, since "Chukah" does not allow for error there.

It must be the Matanos of the Par bi'F'nim before the Goralos, thus indicating R. Shimon's position that the Goralos are not Me'akev.

Alternately, it could be R. Yehudah's position, and while the order is not Me'akev, Hagralah is.

We see the positions of R. Shimon and R. Yehudah regarding the indispensable nature of Vidui inferred from the Beraisa.

The Pasuk "Yo'omad Chai" is understood by R. Yehudah to mean until the Matan Dam of the other Sa'ir, while R. Shimon takes it to mean until the Vidui.

R. Yehudah learns that the Kaparah of the Pasuk is Kaparas Damim while R. Shimon learns that the Kaparah is Devarim.

Question: From R. Akiva's response to his students it seems that (had it not been for our concern over the Tzedukim that) the Goral is not Me'akev (contrary to what we have been taught)?!

Answer: They actually asked about moving the left Sa'ir and the Goral to his right side, and to that R. Akiva said no, because of the Tzedokim.

Question: From the Beraisa (explaining the word "Alav") it seems that Hagralah is Me'akev and that Hanachah is not.

Answer: No, "Alav" teaches that once we know which animal is which, it is purely a Mitzvah to place the Goral on the animal, and still, both Aliyah and Hanachah may not be Me'akev.

Question: The Beraisa (a Sifra-Toras Kohanim) teaches that the Goral makes the Kedushah, and not the Kohen's words?!

This is taught to counter the effect of a Kal va'Chomer which one might encourage us to learn that the Name should make it a Chatas.

The Pasuk thus teaches that it is the Goral creating the Chatas, and not the Name.

An unnamed Sifra is the position of R. Yehudah.

We thus resolve conclusively in favor of those who hold that Hagralah is Me'akev.