ugh....Why does this sound more life threatening than dropping the transmission?
I feel the need to add just a bit more info for you munch on.
You hadn't mentioned that you have seperated the ball joint from the spindal yet. So...
just loosen the nut on the upper joint after taking the cotter key out. Almost all the way, but leave a few threads still on it. Now with a bfh or a joint seperaer, smack the thing loose. I.E.. either hitting the side of the hub assembly or the ball joint fork. Once the pressure is unloaded off the ball joint (it is a taper shaft) , use a floor jack on the lower control arm and lift the assembly up a bit so you can take the weight off the upper assembly. Now notice the upper joint has a boot attached. Useing a screw driver (flat tip) pry the boot down. It is also attached on to the thread area and will make it hard to unscrew if you leave it on. Then as CP said, leave the upper control arm on and also leave the nut on a bit when unscrewing. This will keep it centered better and make it just a wee bit easier. And if you had a 1/2 impact gun it would be easier, but if you don't, follow up on what the other guys said about leverage.
This is a self taping joint, so you don't want to cross thread the new joint in. And throw some grease on the threads when re installing.