Congratulations you've now gotten to the hard part! :whipping2
I cut the top off the ball with a Dremel tool (and hacksaw when that broke), and then used a large socket on the top to press it out with the 3 jaw puller. I put a bolt in the top of the socket to give the puller screw something to set on.
Soak it with penetrating oil, and then put some pressure on it with the puller and hit it around the edges with a hammer. Give the top of the puller a smack too if you can get on it. Then tighten it some more. Mine were tight, but they came out using a puller just like the one you have.
Then, I bought the ball joint kit from Harbor Freight, which won't work on its own, but does have the spacers you need to use the press to put the new ones in.
And, it just so happens I took a few pictures. :cheers:
Cut off:
Large Socket (this worked, but one just a little larger would have been better, an impact socket that size would probably be ideal, with the thicker walls)
Pressing the new one in with the HF junk:
Good luck.