It's a really a red herring to talk about "strict" readings of the Constitution. The issue is honest readings. It's like I said in my other posts - the purpose of the first amendment is to protect people's rights, not their sensibilities. When it talks about "no law", it's referring to laws - that is, official edicts that have real-world effects, such as benefits of some kind, or simple restriction of behavior. It requires a great deal of creative - that is to say, dishonest - interpretation to say it restricts government from making an expression, especially when the courts apply that interpretation in a highly selective manner.
Judge Moore made that same argument, but the question has previously been asked and answered by the US Supreme Court.
Their logic is not hard to follow, even if you disagree with it. It goes something like this: If a law authorizing the government to do something is unconstitutional, then that same action by the government in the absence of such a law is also unconstitutional.
Would a law requiring the installation of Judge Moore's monument in that courthouse be unconstitutional?