Now to get from 14,000 to 7,000,000 would mean an average of 500 shares per account. That seems unreasonable

That doesn’t seem that unreasonable to me. Everyone has 2^n great-great-grandparents, and that means a lot of cousins, uncles, aunts, etc. You don’t have to go back many generations to reach a very large number of relatives. I think that’s one of the cool things about genealogy.