You're probably right about the personal material, although I suspect you could make the theoretical points in another way. But it wouldn't be a matter of easily substituting one thing for another.

One could make the points about religious beliefs relative to rationality without directly asserting that all religious beliefs are false, simply because it is obvious for simple logical reasons that the majority of such beliefs are false (because opposed religious beliefs cannot both be true), and even religious people will grant that this is the case. And the majority of such beliefs being false means that if you actually want to know the truth, you need to take a lot more care about such things than most people do, whether or not any religious beliefs are actually true.

The same general point is actually true about anti-religious beliefs as well, and this may be one reason why that wouldn't be a book Eliezer could have written. For example, he said that he would rather push a button that would destroy the world if God exists, than a button that had a known probability of one in a billion of destroying the world.

It seems to me more reasonable to believe that Mohammed or Joseph Smith was a prophet from God, than to push that "destroy the world if God exists" button. In other words, Eliezer's personal beliefs are unreasonable in a similar way, just in an opposite direction.