Success!

The key was that the ball joint was restricted from traveling up the female shaft on the steering knuckle by caked sealant / epoxy (squirted in there to prevent rust). Looking from below, the dome of the female shaft looks just like metal, but in fact chipped out as epoxy.

Once I got that stuff off, the techniques you guys recommended for getting enough leverage worked great.

Now the only question is: What should I use as a sealant, to squirt in the gap between the arms of the pinch joint?