Just the jacks would work. Lower the camper as far as possible.
However, that is pretty hard on the jack mounts and there will be some sway.
If you can support the camper base in one of the ways you described, you can eliminate all sway and all bending forces from the jacks. After you have supported the base and lowered the camper onto the supports, just lift each jack gently until it is barely free from the ground to remove any built up tension, then drop it again without lifting the camper.
There is also a product called Wobble Stoppers by Torklift that adds additional bracing to the jacks and eliminates sway without supports underneath the camper.
Edit: The camper is 15 years old - the front jack mounts may not be as solid as they once were. Or they may be as good as new - I don't know your camper.