Naphtali Yegear in Shar Yashuv, the yeshiva of Rav Freifeld when I was there did a lot of work on Ketuboth page 9 where this all comes up in Tosphot. The basic issue there is the fact that a Cohen finds his bride not to be a virgin, she is forbidden to him. The reason is we do not know if the act of sex happened before the kidushin or afterwards [in those days there was a long wait between kidushin and Hupa]. If it was after Kidushin then she is forbidden even if it was rape. Tosphot asks why not go with חזקת כשרות? Answer: On the contrary חזקת הגוף
The truth is I am not sure what Tosphot means here. I think he means חזקת הגוף is what we normally call חזקא מעיקרא and that just like the mikve in Nida page 2 we would put חזקה דהשתא together with and another חזקה and together they have the power to defeat a חזקה מעיקרא. Thus she would be permitted to her husband.
But if so what is Tosphot answering? That חזקה מעיקרא can defeat both חזקה דהשתא along with חזקת כשרות? That is I think not what Tosphot means. Rather I think he means that those two חזקות can not defeat חזקה מעיקרא but they can make the whole situation into a doubt. And after all that is all we are looking for in Ketubot.
I noticed Rav Shach says when there is a doubt the חזקת השתא and חזקה מעיקרא cancel each other, and if you combine some other חזקה with חזקת השתא then you get a וודאי. But when there is no reason to start doubting anything in the first place, then you only look at חזקה מעיקרא and not at חזקת השתא at all. He also ties this with an argument between Rav and Shmuel.
I am not sure if this change anything in our case here in Bava Metzia.
What I mean is that Rav Shach and R.Akiva Eigger disagree about the reason the wife of the cohen is forbidden to him. Tosphot brings two contrary חזקות and R Akiva Eiger asks why not add חזקה דהשתא to the חזקת כשרות to allow her? He answers צירוף חזקות only works if they both indicate the same thing. Rav Shach answers a different answer as I mentioned up above. You need to start with a doubt when the crucial event took place. How doe this relate to the way I look at Bava Metzia page 100? There we have 4 חזקות, two against two.
The way I think we can look at this is this. The Gemara puts the calf into an alley. Then the חזקה that determines ownership should be מרא קמא. And to the Gemara that would work except for the fact that the mishna is Sumchos. So I wonder why not bring in חזקה מעיקרא here to tell us the birth came later and to make ownership a doubt so the mishna could be the sages also? The way I have been thinking for about 24 hours is that this is the argument between the Ri and the Rashbam. The Ri holds we have a doubt about when the calf was born and so חזקה דהשתא וחזקה מעיקרא mutually cancel. The Rashba holds until the animal was born there was no reason to doubt when it will be born. It is not like the mikve that is constantly getting less over a period of time and thus we have a doubt when it go to be less that 40 seah.