Close to shekels they will fall to shekels, to charity they will fall to charity

I don’t think this is a blasphemy, but it certainly seems to me to be a logical and correct interpretation. The Mishnah and the Maimonides, following it, bring here the law of proximity. The innovation is that law of proximity also exists in prohibition and permission and in money. They did not enter into practical questions here, what happens if one of the parties has a majority, and what if the currency is similar to those in one pile and different from those in the other pile (perhaps one is shekels and the other is dollars), etc. This is the way of the Talmud, and hence the need for validity. I do not see this as a real difficulty. By the way, in light of what I explained in my article on validity, you will understand that even those who put equal piles do not really mean to say that this is what the Mishnah was dealing with. Their intention is to say that the Mishnah came to renew law of proximity. And when you ask what about majority, it will be established that it is equal piles. But the innovation is always true, even when the piles are not equal: that law of proximity is relevant in these situations as well. See my article there.