This may take a whole different style of training, because it becomes more of a sustained "sprint" to run a 3:20 or 3:30. While speed would be important, you would have to have slow-twitch and intermediate muscle fibers which could sustain maximum effort. CNS fatigue would become a major factor. If you look up the central governor theory, you will find that the mind tends to limit full recruitment of all muscle cells except in extreme emergencies (i.e., running from a threat). Very little has been done to explore ways to train and improve this threshold of "mental shutdown" of muscles.
There is evidence, in the form of fossilized footprints, that prehistoric men could run faster than the peak speed of Usain Bolt, so it is not beyond the realm of possibility that a faster mile has been run. However, there were many more circumstances in which prehistoric men would have run under duress.