Nick has an idea and I shall now illustrate it:
Depending on where we choose to open the mine, whether ontop of a mountain or on the side of it/a hill, we can set it up as follows. After we hit the bottom, we can build a way for minecarts to go up and down the shaft. After hitting the bottom, we go off in either two or four directions, most likely two at the beginning. On the walls above the bottom, we could open up other shafts. Each miner could be responsible for his own shaft of the mine. With all the spare cobblestone dug out from doing this, we'd have enough picks to last them ages.
Minecarts going up: are you crazy? Unless we get self propelling soon that isn't happening.
A water elevator is simpler and protects from lava influx.
EDIT: I did a quick strip mine test and was able to get down 8 layers in the period of one night and day.
Assuming a height of 48, we have 6 people mine and 1 person do above ground stuff (get wood, mostly, but also pig meat)