I had a car one time that was like that. The manufacturer had made the inside diameter of the head too tight. Causing the packing to squeeze the piston too tightly. That car they replaced the head with one machined to the right tolerances.
Maybe just sand the piston where it will actually be touched by the packing when the cars at a floor. Might get just enough oil to be carried onto the packing without sanding the entire piston. That being said, I've never had to sand one to "fix" anything.
What about putting some Maxglide in the oil (add some to the jack/jacks directly)? I've had good success on cars with sticky packings with it. And if it doesn't work you won't have harmed anything.