Before you do anything, mark the current position of the soundpost (providing that is the sound you like). To do this, tape a pencil to a long object (like a wooden spoon!?*#!!), go in through the F hole and trace a light pencil mark around the base of the soundpost. Why? So if all fails ant the post falls over, you know where to put it back in.
As for removing all strings at ones, keep some pressure on top of the bass: I like to make a little pile of books roughly same height as the bridge and tighten a couple of the strings on top, so the minimum of pressure prevents the post from falling. As already suggested, you need to keep the bass on its back.