Beating on the control arm with a sledge hammer hasn't worked. Looking closely at the portion of the steering knuckle into which the outer ball joint fits looks to me as if the recess is open to the top. So, if I remove the axle can I beat on the ball joint from above?

 

Even in the rust free PNW, I had to buy the cheapo HF separator. It is actually not too bad. You might have to load up the separator and still have to smash the control arm on the side.

You can beat the joint from above but you need to set up a solid support on the arm to do that.

 

That should work to get it out of the knuckle. I used, a chisel, flat bladed screwdriver, hammer, and some cursing. You might avoid pulling the axle if you use a long punch or screwdriver. I put some antiseize between the ball joint and the steering knuckle so hopefully it'll come apart easier next time.

 

What worked for me was to remove the knuckle entirely, put it in a vise, and use a long socket extension through the strut hole to bash the ball joint out from above. Yes, removing the knuckle takes time to do but it saves time in the long run compared to trying to chisel the joint out.