You are correct.  There is no substitute to removing that shaft.  The pusher is the best option.  You can fabricate one using the photos as a guide.  I tried to find one I could purchase but couldn't find one beefy enough online.  The one pictured is home make and looks similar in size and shape to the one the boat yard used on mine.  Make sure the upper portions "bear" on the hollow shaft so you are pushing the solid inner-shaft with counter pressure against the hollow shaft onto which the bronze gear mounts.