At any rate, if the former is true, 2+2=4 is outside the province of empirical science, and applying empirical reasoning to evaluate its 'truth' is wrong.

When I imagine putting two apples next to two apples, I can predict what will actually happen when I put two earplugs next to two earplugs, and indeed, my mind can store the result in a generalized fashion which makes predictions in many specific instances. If you do not call this useful abstract belief "2 + 2 = 4", I should like to know what you call it. If the belief is outside the province of empirical science, I would like to know why it makes such good predictions.

To apply the same reasoning the other way, if you aren't a Christian, what would be a situation which would convince you of the truth of Christianity?

You'd have to fix all the problems in belief, one by one, by reversing the evidence that originally convinced me of the beliefs' negations. If the Sun stopped in the sky for a day, and then Earth's rotation restarted without apparent damage, that would convince me there was one heck of a powerful entity in the neighborhood. It wouldn't show the entity was God, which would be much more complicated, but it's an example of how one small piece of my model could be flipped from the negation of Christianity (in that facet) to the non-negation.

Getting all the pieces of the factual model (including the parts I was previously convinced were logically self-contradictory) to align with Christianity's factual model, would still leave all the ethical problems. So the actual end result would be to convince me that the universe was in the hands of a monstrously insane and vicious God. But then there does not need to be any observable situation which convinces me that it is morally acceptable to murder the first-born children of Egyptians - morality does not come from environmental entanglement.