I think your biggest issue, is with holding everything steady enough to get the pin out.
Not knowing what all you have, I would suggest a deep well socket held in a vise, and use it to support the reel, while you holed the reel, and a punch with one hand, and a hammer in the other.
If you have a drill press vise, I would then mount the deep well socket in the DP vise, and set it on the drill press, with the punch held in the chuck. Then you can hold the reel with one hand, and work the quill feed with the other. You can get lots of pressure and control that way.
For more force, and control, I would cut a punch working end down to just enough to get things started, and then use another to finish getting the pin out.
Still against the drill press, I would then look at an arbor press. You could cut your punch handles down to 1 to 2 inches. Drill a 1/2 to 1&1/2 inch hole in the working end of the arbor press, the you can just hold the punches enough to get things lined up, and then things will stay in place. Still using a deep well socket, or piece of pipe to support the bottom side of the reel.
Think outside the box. think about holding & supporting the bottom side. Then think of how to get the pressure on the pin. Look around, and see what you have available to accomplish this.