The argument in your last paragraph is not very convincing. Maybe you do need to "get into deism and prime movers", after all. That paragaph basically asserts that anything, which is "built upon" a disproven source, fails to justify belief in its truth. Okay, fair enough; but only if we stay focused on what "built upon" means in your context. It means "depends upon", "relies upon", "follows from", and so forth, in a logical sense.

Similarly, it only means "[couldn't] have ever existed without" if that phrase is understood from a logical standpoint ... instead of, say, a historical standpoint, a scientific standpoint, etc. In other words, while it might possibly be true--though I wouldn't bet on it--that historical factors or some law of science, to name two off-topic examples, could everywhere force pan-spiritualism to be born chronologically after organized religion, those things are beyond the scope of your argument. You're relying on logic. Not history, not science, etc.

And now we get to my problem: I'm afraid I must report that no cases of pan-spiritualism that I've encountered have tenets that, strictly speaking, logically depend upon, rely upon, or follow from those of any organized religion, in any instance I've ever observed. Indeed, pan-spiritualism, as I know it, entails so much abstraction, that one could just as "easily" say it builds on any other belief system you might name, e.g., Santa Claus at the North Pole, loop quantum gravity, seeding by Celestials per Marvel Comics, M-Theory, or whatever! What all this amounts to is that pan-spiritualism really builds on nothing; or else, if we now do relax our definition of "built upon", it builds on countless things that seem like a complex blend of hard truth and daft falsehood, simultaneously.