I'm sure the body bushings are wiped out and are contributing to the flex.
When I was in the shop, I always put the pads as far forward on the front stub frame, behind the front wheels, as possible. And the rear pads always went on the leaf spring front mounts just ahead of the rear wheels.
Some flex is to be expected - all cars do it.
Unless you need the doors open, leave them closed, or open them before you lift.