Through long debate and lots of headaches we came up with a solution that would work. It is a combination of our two previous solutions. This solution involves a set of planetary ratchets with a ratchet on both the top and the bottom, with the ratchets facing opposite directions. The ratchets and planetary gears move as a unit either up or down when the clutch is pulled. The entire unit of ratchets and gears is inside an outer shell. The outer shell has the gear that the ratchets latch onto. When the clutch is pulled it pulls the entire set of gears and ratchets into the reverse direction, and when it is released it has a spring to pull it back into the forward position.
So far we have modeled the planetary gears, the gear cage and the ratchets. We are thinking that we are going to end up milling a lot of the parts out of aluminum, but reuse as many of the bike parts as we can. We are starting to feel the time pressure of the end of school and are working hard!