My question is, what about inventors? The person who came up with the couch, wheel, table, iPod? Does an "inventor" as such even exist?

I think Plato accredits inventors with the ingenuity to look inside their own soul.  Plato says in The Republic that by looking into our souls, we can see and grasp ideas from the world of forms.  While Plato may not actually call those people inventors, I would say that those people and their work would be the type of professions he valued the most, simply because they introduced products and ideas with original value, as far as the real, physical world is concerned.  However, I would say that he would not refer to them as inventors.  If Plato believed that every original idea came from the world of forms than that would imply the preexistence of everything created in the real, physical world.  While he may not acknowledge these inventors as actual "inventors," I think he certainly would speak highly of their productive nature and their valuable contributions to society.