Just to be clear, there are two versions of 6105 drive unit design, 2008-2012 the drive shaft is removable, it has a blue bushing on each end and the shaft reaches the front cover. On the version made since 2012 the shaft is a permanent part of the motor and does not pass through the front of the drive unit.
If the shaft is a permanent type and has come out your best bet is to tap it in with a hammer after getting everything clean and dry and using a drop of super glue on the end of the shaft seated in the motor. How permenant this repair will be depends on how badly worn or damaged the shaft seat is.
For the shaft stuck in the drive unit, I generally use either a suitably sized nail and hammer to drive it out, or carefully grab an end that will not have the impeller in contact with it and pull it out with pliers, a twisting motion will tend to help and you can take breaks if it gets stuck and try soaks in vinegar for several hours.