I agree with your criticism, but I don't get what is the problem with the first point (I am not a native speaker). Doesn't "nearly" just mean "close to" and not necessarily "less than"?
It is still no clear to me what makes "nearly" in this particular case to mean "less than". Curiously enough, "nearly crossed the finish line" indeed sounds totally wrong to me.
That said, I believe it is usually used to mean "less than". In this case, I would use "just over" instead, ie, "closed, it's just over double that".