Going through again and thought of problem: R. Eliezer said in our mishnah zman Kriat Sh'ma is from the time the Kohanim ENTER to eat their trumah and on 2B he says when the day is sanctified erev shabbat, which I would think is thus the same time. My theory: the time of R. Yehoshua, when they are PURIFIED, perhaps goes like R. Yosi like an eye's blink before tzeit hachochavim, the bein hashemashot. But they don't actually come in to eat until after tzeit, which is a very short period of time anyway. And we could still say that ani and Kohanim ENTERING and kideish hayom are chad shiura hu.
Natan
Dear Natan.
I think you didn't notice the Gemara on 3a, which distinctly maintains that Rebbi Eliezer in our Mishnah and Rebbi Eliezer in the Beraisa are two different opinions. Tosfos adds that they cannot be one and the same, because if they were, then Rebbi Eliezer in the Beraisa would be saying the same as Rebbi Yehoshua (who holds like Rebbi Eliezer in the Mishnah).
Aside from that, one cannot possibly say that Ani and Kohen are one and the same Shi'ur, since the Gemara initially suggests it, but concludes that they are not.
Kindest regards
Eliezer Chrysler