If you want it, here's the device you'll need:

That machine is worth saving every part. Try a couple of drops of liquid wrench over and around the spline bolt and let it soak in overnight. Then do the boiling turban the next morning and try to wrap the towels tightly around the top of the agitator to concentrate the heat and steam where they are most effective.  Good luck and I expect pictures of that Super Duper Surgilator when you are able to extract it from the machine. Also, when you do get it out, try gently grinding or wire-brushing the rust off of the spline and applying a little white grease or some other lubricant to stop the rust.