Meilah 6b, 8a - zerikah for pigul nosar v'tamei

Whenever the mishnah mentions (Me’ilah 6b, 8a) zerikah taking off me'ilah, Tosefos says that the simple reading is if you hold, heiter achilah shaninu. But if you hold heiter zerikah shaninu, you have to read it like this: zerikah means, rauy l'zerikah. And if you hold heiter shechitah shaninu, you read it another way, that the kabbalah was not done right so that me’ilah lasts until the zerikah.
I'm confused. Both these mishnayos, on 6b and 8a, say that a second thing happens with zerikah: The dinim of pigul, nosar, and tamei. Are those things part of the machlokes as well? Surely everyone agrees that those only happen with the actual zerikah? If so, everyone else (at least the man d’amar heter zerikah shaninu) needs to read the mishnah in a very difficult way, l'tzedadim.
Why doesn't the gemara (or the rishonim) bring these mishnayos as evidence that heiter achilah shaninu?

R' Tzvi Berkowitz shlit"a pointed out to me the Tosefos on 8a:
The divrei hamaschil of Tosefos implies that they are saying that these alternate cases do indeed apply to the whole set of cases there, including the chiuvim of pigul, nosar, and tamei - not just that there is no me'ilah.
I later saw that there is a Rashash who suggests this possibility.
So I guess this isn't a kashya, it's just true.

My son Yehudah n"y says that there is a Reb Chaim al haShas that brings a similar type of issue with regard to birds (chatas) in the later mishnah: The gemara discusses whether the mishnah is saying mitzuy or haza'ah (squeezing out the blood or sprinkling it). The issue apparently is, Is mitzuy ma'ekev, required, or optional.
According to Reb Chaim, this is only for the issue of pigul, nosar, and tamei, also there in the mishnah, but for me'ilah everyone agrees that the mishnah is saying haza'ah.