Rav Meir pointed out that there is a difficulty understanding what is the answer of the gemara about why kohanim are chayav. The answer given in shiur is that the sukka does not create a problem for teshvu ke'in taduru but something external to that, that they have a tahara issue. The Rema seems to use this idea to say that the problem today (or back when he wrote it) IS inherent to the sukka (to justify not sleeping there), as he does not have a "sukka meyuchedes" for him and his wife. However, the Gr"a and others disagree with this and say, (if i understood this correctly), that Tosfos and Rashi that teshvu kein taduru is not me'akev!! (this is for sure what the "chok nasan" in the back of the gemara says).
One interesting question raised on this, by the Cheshek Shlomo (again in likutim in back of the gemara), is what about a yisrael -- he also is chayav in reiyas panim in the azara and therefore needs to be in a state of tahara! He suggests that mitzvas reiyas panim is only on the first day and simchas yom tov after that would be with כסות נקיה and ייו ישן. And in terms of the first night, he says that one would not get hte petur of the first night based on teshvu ke'in taduru since you are chayav the first night also because of hekesh to pesach!