Best to pull the assembly out of the car and take it to the workbench or a press.
I once considered creating a support under the thing from the cars floor. Cinder block, scraps of wood, whatever, all seemed too much effort to be a true shortcut.
I removed the hole assembly out of the my car as RedFish is suggesting , it was easy and it only took me about hour and half to remove and change the handle , then reassembly it back in the car.