Don't ask me to make sense of it.

To me it seems nonsense on multiple levels. If anything ceremony makes something more religious, not less. The original meaning of the word ceremony was religious observance. Same with repetition. The lord's prayer and the schema and the shahada haven't become less religious through centuries of repetition, and "In God We Trust" is the same kind of profession of faith. Nor do I see how any of this would be an antidote for the overt religious meaning. The 1st amendment doesn't carve out an exception based on repetition.

Or if the motto was "America, God Damn It's A Big Country", then perhaps you could argue the use of "God" was incidental. But here there's no meaning other than the religious meaning. There's nothing else that it's conceivably adding ceremonial gravity to, there's just the promotion of religion.

And on top of all of that, it's obviously a pretense. The original intention of including these phrases isn't obscure, it was religion versus "Atheist Communism". Today it's more generally about religion versus secularism, but then and now it's always been about promoting religious dominionism.