I've heard of people fastening braided steel wire to the inboard side using a screw band clamp or something simliar, leaving an extra length of a foot or two, putting the length in a 3lb sledge and swinging the sledge away from the axle using the wire and the moving mass of the BFH to pull it out instead of pushing.
I can't say that I've done it myself, but it sounds like it would work.
You could also pry the shaft out using a pry bar of some sort but you risk damaging your differential housing if it's not done right.