You contrast "substance" to "ideas," but I think you mean something like "appearances" (rather than "substance.") For Plato, the Ideas *are* the substance, that is, the underlying reality (the essence) of the  world of physical phenomena. 

Source: https://plato.stanford.edu/entries/substance/

"Forms are Plato’s substances, for everything derives its existence from Forms."

As you acknowledge, a human being is made up of matter (the physical body), and spirit (the soul/mind). Spirit is immaterial (which is why some empiricists, Dennett for example, stupidly deny its existence—the soul cannot be an object of modern empirical science because it is not a part of the physical world) and thus has no extension in space. As such, it is mistaken to speak of spiritual "spaces" in a literal sense (which misspeaking would be a prime example of confusing the map with the territory).

Moreover, at the end of the day, Plato was essentially right. Spirit is a more primary reality than matter, because all material entities depend on immaterial entities. 

One proof of this is that modern science, which functions quite well, could not function without taking as a kind of axiom the fact that immaterial laws govern the world of observable physical phenomena. 

That is, a scientist observes examples of a material, tangible phenomenon multiple times and abstracts from these incidents an immaterial, spiritual reality, a scientific law, which they propose governs the incidence of this phenomenon. 

In other words, these material phenomena *depend* on immaterial things (if the law did not really exist, the phenomenon would not occur).

No one has ever empirically observed a scientific law in the material (physical) world! Rather, science functions through a scientist's inference of a (spiritual) law from the physical phenomena he or she observes.

Don't confuse the word "spiritual" to mean inherently or essentially vague. That may be the postmodern connotation of it, but in themselves, spiritual realities are more distinct, have more being to them, because they are higher in the chain of being (to use a material metaphor!) than physical realities (again, because of the aforementioned relationship of dependence; a being which depends on another being is lesser than the being on which it depends).

I think that your point of view on the soul (emergent materialism) possibly entails that it is extinguished by physical death. I am not able to prove, using reason alone, that the soul is immortal. But I do think that a mortal soul would jar with the general tendency of being (that spiritual beings are greater and less perishable or mutable than material beings).

Yet it does seem that there are examples of spirit depending on matter. None of us remember what it was like before we were born. This doesn't prove anything, but it does point towards us not existing, even in spirit, before we were physically conceived (and thus depending on physical beings in order to exist). 

Without some physical medium of communication, human beings are unable to communicate with one another. Thus if two people communicate, person B's reception of person A's idea (that is, the presence of person A's idea, which is a spiritual being, in their soul), depends at least in part on some physical thing.

So from the perspective of natural reason, I think that the soul's mortality is, sadly, somewhat defensible. At least I can say that its opposite, to the best of my understanding, cannot be conclusively established through a deductive argument (like the existence and superiority of immaterial beings).