I've had GREAT success using my cherry picker and renting another one from a tool rental place.
I've removed the bodies on a '56 Chevy 2dr post, and a '57 Chevy 2dr station wagon.
I jacked the body up off the frame with my floor jack, just far enough to get a 4x4 beam under the body as far forward as I could, and as close to the rear wheel opening as I could.
Each 4x4 had a very stout eye-bolt through the ends. The bolts were drilled all the way through and secured with nuts and BIG washers. I didn't trust using the lag-bolt style threaded eye-bolts, for fear the threads would pull out of the wood.
I ran a longish chain from the eye-bolt in front to the eye-bolt in back, on both sides. Then I slid the cherry pickers in on both sides of the car and lifted from the center of the chains. On the sedan, it worked VERY well. On the wagon, with all the rear overhang, the car wanted to tip backwards, so a neighbor was employed to hold the back end of the car up while we rolled the old chassis out and the new, finished chassis in. All told, the whole procedure took under 20 minutes to swap chassis on the wagon.
The key is that second cherry picker.
-Brad