Interesting discussion - especially the descriptions of Fi. I'll just throw this out there.
Is it possible that Fi permeates the subconscious, but as a judging function is somewhat steered from the conscious mind? A bit like a ship on the ocean?
And then Ni and/or Ne also permeates the subconscious, but as a perceiving function tends to be driven from beneath its waters like a deep ocean current?
In this way it is difficult to compare which sits more deeply in the whole of the mind because it might even depend on the individual. What do you think?
Edit: Just something else to consider: I wouldn't underestimate just how much Se and possibly Si uses the subconscious. It is an established fact that our minds take in far more information through our senses than what our conscious mind processes. Think of the concept of intuitive physics like when a racecar driver responds to concrete stimuli faster than it could be described. Same is true for firefighters, martial artists, musicians, etc. One big aspect of learning complex music is to be able to internalize most of it so that you don't have to consciously process it. That aspect could be Si, and then consider improvisors who create complex ideas instantaneously which could be Se.
The only functions I have trouble relating to the subconscious are Ti/Te, but that is not to say these do not have an interesting relationship that does employ its use.