I think "Age of Discovery or Renaissance" are good category names for a group of the techs commonly invented in Europe between 1500-1700.Sorry, but these proposals are not more civ-neutral. Age of Reason seems to cover something that has happened more than once (the first time that we know of during the Golden Age of Athens), Age of Discovery is no less eurocentric than Renaissance, Age of Enlightenment is not that different from Age of Reason.
The middle ages is smack in the middle of the classical era and the Renaissance, and will probably never be renamed. Antiquity will never become a weird name for a period that was far back in time. The relative name "Modern era" is a name preserved for the present era, and is just a placeholder until it can get a retrospective name that will be absolute. The same can not be said about antiquity or the middle ages. If history class, 500 years in the future, use the name modern era about today, it would astound me.Iron Age does not cover civilizations where there is no iron, Antiquity and Middle Ages has the same long-term problem that Modern Age has (but far less urgent - I think it would take centuries if not millenia to really question what should be called "Middle Ages"). The early eras are clearly not eurocentric, so you might say every age is somewhat defined by the first culture group to reach that point.
It is true that nations that didn't have iron available stagnated technologically and remained in the copper era; there are many more examples such as a lack of work animals in america preventing them from entering the classical era.
I really don't want civ to simulate this too much.
Regions that skipped such an era would in civ terms either have bought a lot of the techs in that era or been conquered by a more technologically advanced civ.