Basically, Ne seeks to change or reinvent the external object, idea, theory, person, etc.
Ni seeks to change or reinvent your personal perceptions of it--Ni questions the process of perception itself and the possible flaws therein. It does not actually interact directly with the external idea or object. Ni is far more personal and cannot easily be explained or expressed to others the way Ne can. (Nor does it even want external validation the way Ne usually does.)
Nice way to re-state it.
I agree with the phrase "re-invent" from the Introvert's POV. (The extrovert is far more apt to try to "change" something via Ne, that's ENxP in a nutshell; INxP is going to re-invent or re-cast the inherent definition of the object, changing its essence and context in the Ji scheme of things.)
"Hey Capa -- We're only stardust." ~ "Sunshine"
“Pleasure to me is wonder—the unexplored, the unexpected, the thing that is hidden and the changeless thing that lurks behind superficial mutability. To trace the remote in the immediate; the eternal in the ephemeral; the past in the present; the infinite in the finite; these are to me the springs of delight and beauty.” ~ H.P. Lovecraft