I share your difficulties with reading music and transposing. However, I doubt that the reason is that your (or my) mind is too highly trained. Instead, I think that people who have trouble sight-reading simply have not made the transition from a conscious processing of the musical notation to a state of automaticity in which the low-level details of interpreting the musical notation are performed by the brain unconsciously. I am curious; as a child did you study with a piano teacher or are you self taught? I suspect that one of the purposes of formal piano lessons (and all the practicing that lessons entail) is to make the interpretation of the notation automatic; as you point out, the notation is complex enough that most people won’t be able to interpret it consciously in real-time with enough fluidity as to produce anything very musical.
It is worth noting that some very accomplished musicians never learned to read music (albeit probably no accomplished classical musicians who would presumably need to be able to read notation). Unfortunately I can’t come up with any examples, but it is common enough when reading about blues, folk, jazz or rock musicians to read about musicians that never learned to read music. So, I think that being able to produce music and being able to read the notation are two separate, albeit related, skills.