A year and a half ago, I predicted on this basis that there would be 108 chapters total.

I was wrong, but another piece of evidence against coincidence is that the lower bound on horcruxes makes for the second instance of 107 in Eliezer's fiction. The first is here, as follows:

The wise fool gave the young genie exactly one hundred and seven precautions to follow while making people happy. The wise fool thought that, with such a long list as that, he was being very careful.