I didn’t cite that as proof of intentional theocracy. You made that up.
But the references are there and they are proof of what most of the founding fathers believed.
The word “blessing” and the use of A.D. are proof of nothing of the kind. They would have had to be crazy to reject A.D. in particular when it was the only thing anyone ever used at that time for what some now call C.E.
We know they worshipped God, because of other sources. The idea that the use of “blessing” and “AD” is some kind of dogwhistle to the believers is preposterous.