[Greg]

I think that part is meant to be a permanent part of the switch.

I took a look at one I had lying around. The wafer with the stationary contacts appears to have "fingers" holding the "rotor" in place. I marked one in the picture below (you can see one):
   

Maybe you damaged one or more fingers and it got loose? I kind of thought the engaged contacts would have held it in place (would think there are some for each position).

I suspect it would be possible to replace it and the contacts would hold it in place long enough to get the shaft put in place. You have to figure out how to not put it in "backwards". Even if the fingers are busted, the contacts may be enough to keep it from "wandering" on the shaft? Just guessing...

Is that the last one of the lot? If so, maybe that's why the shaft finally went in.