If we had a diagram of your device, one might suggest changing the gear ratio so that you get faster movement. However, when you increase speed with gears, you lose torque. Not sure if you have enough reserve power from your drill motor to do this or not.
If you are powering the drill motor from the same supply as used on the drill, you will not want to increase current or voltage. It is most likely already using it's maximum capability.
Another alternative is to get a motor with a higher rpm rating.
MP