The problem was not getting things apart, but rather getting them put back together. The only way I could get things back in place was to use a long pry bar to force the control arm down. I tried spring compressors, bottle jacks, and floor jacks, but the long pry bar was the only thing that worked.
Later on in life, I replaced the ball joints, and installed joints that bolt in place, rather than being riveted in. With the new ball joints, I can loosen the bolts enough to drop the ball joint half an inch or so, which makes the re-install much easier.