Also the spice is never deemed a path to salvation. it is merely an integral ressource that is stabilizing the human order by mutual dependence. In the later books the problem is explored what happens when the ressource becomes less integral/more abundant, removing the mutual dependence.
I don't really agree that the spice wasn't put forward as a way to salvation. I think it clearly was key to finding the golden path.
The spice enabled the Bene Gesserit to see what was needed in their breeding program, and they were trying to breed Kwisatz Haderach who would lead humanity through a dangerous time, avoiding the destruction of the race. (Also the scene in the sietch that I won't go into detail about, becuase spoilers)
Leto II uses the spice to see the golden path and forge humanity into what it needs to be to survive. (Also the other thing which I haven't mentioned due to major spoilers of a cool moment).
The spice is pretty clearly necessary for the path taken to salvation.
While the spice may not have been necessary to avoid the destruction of the human race had another path been found, in the story as it was told it was absolutely central.
But that is less the spice and more the prescience. The prescience that failed Paul. Leto II seemed to be clear for the golden path not from the self fullfilling lock-in that prescience created, but from his ability to mediate the other voices he incurred from the spice agony.
Something the Bene Gesserit thought only women to be capeable off, but never managed to put to the effect like Leto II could.
Also Leto II was the tyrant and very explicit about his choice of tyranny as the mean to create the golden path, so certainly not a salvation from imperial nonsense.
So i'd say the spice to be crucial in fullfilling many purposes, but it was never the path to salvation itself and it created many more problems along the way.
The spice is the source of the prescience, I don't think you can draw a line between them (the Tleilaxu could, but even then I think they used what they called synthetic spice, I don't really recall that very well though).
Aside for that point, yep, I agree with pretty much everything you said!