I'm convinced that Moore wanted to use the straight forward argument that no religion was established AND that the Alabama constitution says that Almighty God is the ultimate authority.
This is the most important argument BECAUSE it's "in their face" about the conflict being brought about in our society due to Federal imposition of the religion of "non-religion."
I also like the "free expression" argument. (Since he's charged with decorating the building, he can hang up whatever he wants according to his tastes in art.)
I like the "historical display" argument.
They should use all of them.