I came up with Art Schallock (Yankees), Joe Landrum (Dodgers) and Ray Noble (Giants) once as the possible last three cards, where my reasoning assumed no big names were available. More
HERE if you are interested.
I looked at it again with some possible bigger names and came up with Ralph Kiner, Hal Newhouser and Johnny Logan as possibilities.
Again, more
HERE if interested.
It's interesting that no White Sox players are in the highs.