If all of the above is true (and it is) then why would we not say that the root of conservatism is our belief in God?
Some were devout and some were not. Some were devout in, ways that were not in line with the established church. Certainly their standards of moral conduct varied quite a bit.
You are right to that the nation was founded on Judeo-Christian principles, but I think there was one specific principle that had heavier influence on the founding than the others -- and a principle, furthermore, that was strongly affected by the enlightenment. This is the concept that each person answers to God individually.
In some ways it was a radical concept. The European nations, for the most part, had official churches -- something that was explicitly rejected by the First Amendment. Indeed, the founders rejected an explicit statement of morals in favor of rights (which is why the first ten amendments were called "The Bill of Rights," not "The Bill of Morals."). The rights were God-given -- but in the idea of "natural rights," is the point that they cannot be denied, even by those who do not believe in God.
Those rights exist so that the individual may determine what God wants of him. That is the founding principle that should be the foremost to be concerned. As such, the problem with law based on morals, rather than rights is that they often clash with the founding principle and are, as such, not conservative.
The irony is that the government, founded on Judeo-Christian principles, ought not base its law on Judeo-Christian morals. Rather it should respect the individual relationship (or lack of same, perhaps, in some cases) between man and God and and rule based on rights.
I believe that is what the nation was founded on. I believe, therefore, that it is a conservative, if often radically libertarian, outlook.
(Abortion, BTW, does not fit neatly into this framework, because there is a debate of when the fetus becomes a human individual with the rights of an infant. Even if you think the answer is obvious, the question is presently being debated.)
Whether you have a right to keep and bear arms is currently being debated...does that mean you might not have that right?