Hefsek during yemei nida

The Mishna in Nida on daf 68a quotes a machlokes when the last bedika that shows she's tehora during yemei nida can be in order for it to work. (This isn't halacha l'maase because it's talking about where a nida just counts 7 days and not like we do where all dam is considered ziva.) Rashi understands the Mishna as a three way machlokes and then the gemara on 68b quotes a fourth opinion:
T"k - bedika must be on the seventh day
R' Yehuda - Bedika must be after mincha ketana on the seventh day
Chachamim - Bedika can be as early the second day
Rebbe (on amud beis) - bedika could even be on the first day

Tosafos Harash doesn't like this explanation because it's hard to understand the explanation for the t"k and for the chachamim. He therefore says that the Chachamim are just explaining the t"k. The t"k didn't mean that the bedika had to be in the morning of the seventh day but he was just emphasizing that it didn't have to be at the last minute. Any time she stops bleeding she can do the bedika and the Chachamim really agree with Rebbe that it could even be on hte first day. So why did they say the second day? Tosafos Harash explains that it's just more common. Normally she wouldn't do the bedika on the first day so the chachamim just use that example.

According to Rashi R' Yehuda makes sense. He says that she can't be in chezkas tehara unless she knows that at the end of her yemei nida she wasn't bleeding. Until then she's in chezkas nida. Rebbe makes sense because he says that she just has to prove that she stopped bleeding and then she can assume that no more dam came out otherwise she would have seen or felt it. What is the explanation of the Chachamim and Tana Kama though? I guess that you could understand the Chachamim like the gemara on amud beis understood Rebbe's hava amina. Since it's a mayan pasuach on the first day she can't do a bedika on that day. If that's true though is that a din only on the first day or would the same thing apply on the second day if she bled in the morning then she can't do the bedika in the afternoon? If it's true on the second day would it also be true on the seventh day? I'm almost positive that it wouldn't be true. So why not? The Tana Kama is even harder to understand. I'm guessing that really the t"k agrees with R' Yehuda that the bedika has to be at the end of the yemei nida. Just like R' Yehuda doesn't require her to check straight through bein hashemashos but allows it to be a few hours earlier the t"k says that it can be a few hours earlier than that. Not a great sevara but I can't think of anything better.