1
Of your list of 12, only 3 (Dimaggio, Kiner, Mays) played the majority of their careers outside of the two offensive boom times (nominally the '30s and the '90s).
Edgar was a great hitter with a short career and no defensive value. Edgar is better than many players in the Hall, but I would be surprised if he was ever the best elidgible player outside the Hall.
Kelly