The "church" in "separation of church and state" doesn't imply organization?
You're simply inventing a straw man when you talk about "the level of organization" that's necessary. You can't establish a church that isn't organized, otherwise there's no establishment.
Speaking of being out of step with the persons who wrote the amendment, your continued insistence on equating religion with religious belief does exactly that. Madison defined religion as "the duty which we owe to our Creator, and the manner of discharging it." In other words, mode of worship. And by logical extension, the apparatus surrounding it.
First - as you well know, "separation of church and state" is a shorthand phrase and does not appear in the Founders' discussions of the Constitution prior to ratification.
Second - your insistence that a church must have some undefined level of "organization" to be an "established" state religion is disproved all over the world. There are even many Christian denominations that do not have the level of organization you require.
Third - your reinterpretation of Madison's words borders on the dishonest. I can have duties to my Creator, and discharge those duties, without ever having a single contact with an organized Church. He never said anything about the level of "organization" which would qualify a religion as one which can be "established" and you know it.