With the nut backed off of the ball joint but still on the threads a few turns. Smack it here with your BFH. It wont pop loose right away but this well help loosen the connection. Spray more P.O. if you want, then take your pickle fork, and hammer it in. It should separate the ball joint from the hub, leaving it bolted to the LCA.
If it does not separate,Undo the bottom LCA bolts and come back to it. Proceed to the next step.