Enchanted by tales of "reactionless propulsion", the folks at KSC have invented the momentum tether, an enormous device designed to spin and fling kerbals from one orbit to another. I'm certain it will be a safe and pleasant way to travel.
Create a device to spin+fling Kerbals from a low circular orbit around Ike (13km or as close as is convenient). Spin it up and fling your plucky astronaut to their destination! If you miss but are close, use a maneuver node to figure out ho