1) There is in fact no dispute between Beis Shamai and Beis Hillel about whether a person who is Tamei Sheretz may eat the Korban Pesach in a scenario where most of the Jewish people had become Tamei Mes. We learn this from the Rambam (Hilchos Korban Pesach 7:8) who writes that in such a case the Korban Pesach may be eaten only by those who are Tamei Mes. However, the Rambam then makes an important addition: "ul'ka'Yotzei Bahen Metamei Maga Tumos." The Rambam tells us that it is not only people who touched the corpse who may eat this Korban Pesach, but people who had a similar Tum'ah may also eat the Korban. This similar Tum'ah means that they touched something Tamei. Therefore, when we say that it is only Tamei Mes who can eat the Korban, this does not literally mean only Tamei Mes. It also includes somebody who touched a Sheretz, because the Heter is for any Tum'ah contracted by touching (in contrast to Tum'ah emerging from the body, which is not similar to Tamei Mes at all). So the verse does not only talk about Tum'as Mes according to Beis Hillel.

2) I should add that it is not so clear whether a Tamei Sheretz can indeed eat the Korban Pesach. In fact, in his commentary on the Mishnah in Pesachim 95b, when explaining the Mishnah that our Gemara in Bechoros cites, the Rambam writes the following: "When most of the community have become Tamei specifically to a human corpse, we then say that the Pesach is brought in Tum'ah, and it may be eaten only by Teme'ei Mes, people who have become Tamei to a corpse."

The fact that the Rambam writes that it may be eaten only by Teme'ei Mes suggests that it may not be eaten by a Tamei Sheretz. If so, this contradicts what the Rambam writes in Hilchos Korban Pesach 7:8, as cited above.

(This contradiction is pointed out by Rav Altuski zt'l in Chidushei Basra to Bechoros 33a. Now is not the time or place to try to resolve this contradiction.)

However, let us just think about how our Gemara in Bechoros will fit with the idea that a Tamei Sheretz may not eat the Korban Pesach. The answer is that, again, there will be no dispute between Beis Shamai and Beis Hillel about Tamei Sheretz; everyone will agree that he cannot eat the Korban Pesach. Everyone will agree that it is only Tamei Mes specifically who may eat the Korban Pesach.

So it is not possible to say that Tamei Sheretz can be Machri'a the dispute between Beis Shamai and Beis Hillel, because, on the contrary, we possess no explcit source to tell us whether Tamei Sheretz may eat the Pesach, and it is merely from Sevara that we either compare Tamei Sheretz to Tamei Mes because they are both caused by contact and we say that Tamei Sheretz may eat the Pesach (as the Rambam writes in Hilchos Korban Pesach 7:8), or that we do not compare Tamei Sheretz to Tamei Mes and say that

only Tamei Mes can eat the Pesach. Once we know that Tamei Mes may eat the Pesach, and that one who had Tum'ah emerge from his body may not eat the Pesach, we then must determine to which of these two types of people should Tamei Sheretz be compared. It does not work the opposite way -- namely, that we compare these two kinds of people to Tamei Sheretz.

Kol Tuv,

Dovid Bloom