I think I've finally found it. Maybe. I don't know. There are absolutely TONS of books out there that address the "Christian Nation"/Religion of the Founders topic. I'm not even going name them. You know of many of them. I'll simply note the best, latest one to come out is Stephen Waldman's. My Dad is always asking me when my book is going to come out. I've always answered that the notion that America is not a Christian Nation/what religion did America's Founders believe in? has been done so many times by so many more prominent folks that it would make no sense for me to write such a book until I've found my novel angle.
Maybe I've found it: A legal perspective on why America is not a "Christian Nation." The hoary Holy Trinity case of 1892 once infamously declared in its dicta that America is a Christian nation. My book would be an originalist, legal perspective on why Holy Trinity's dicta was wrong. The holding of the case is quite narrow and even Justice Scalia, in his book A Matter of Interpretation notes that case as wrongly decided and textbook piss poor legal reasoning. Scalia really didn't address the notion that America is a Christian Nation; he just sneered at it, in an aside. That intimated to me that, even he, one of the most conservative members of the Supreme Court wouldn't support the Christian Nation thesis.
The book would be the kind of text that a court, for instance the Supreme Court, could cite as authority, if it ever did have to address the idea of whether the United States is or was founded to be a "Christian Nation."
I know that this is theoretical la la land. I doubt the Supreme Court will ever address the issue and if it does, even the conservatives like Scalia and Thomas probably wouldn't find America to be a "Christian Nation" in a public, civil sense.
But, as a legal claim, it still might be a fun thing to explore. And I'm not aware of any book that quite approaches the Christian Nation question from this angle. Alan Dershowitz's Blasphemy and The Godless Constitution, by Cornell's Kramnick and Moore, both of which I've read, are the closest that come to mind. Those books in many ways only superficially deal with the legal claim. I'd have to make sure I offered something fresh and new. It wouldn't quite be the secular leftist polemics that theirs were. And in a sense I think they overstated their claims, using "law office" history. Mine might be a book that Justices Scalia and Thomas (and the liberals) would find comfortable citing (I doubt the conservatives would with the other two books).
It's just a thought. I've got a book in me on this matter. I'm just waiting till I find my right angle.