I went through my camper shifting every time I went on a trip. I tried all the tricks, tightening the fast guns, rubber mat. My setup is really sensitive to movement because if the camper moves too much, the front Jacks will get in the way of the rear doors on the truck from opening. I have about an inch of clearance.
Part of the reason my camper shifted so much was because I have to raise my camper using a combination of foam, plywood and rubber mats to clear the cab of the truck. Though effective, I think there is just enough bounce in it all that allows the camper to wiggle around.
My solution was to take a 2x12" and notch it to fit the profile of the bed of the truck and the camper itself. I then used some rubber for padding and when the front of the camper is loaded, it sits into this brace tight. No side to side movement is possible. For the back, I only had just over 1" of space between the camper and the sides where the tail gate goes. My solution was just some 1" foam to keep it in place.
The result is a nearly dead perfect centering and it won't shift around to the point that my doors won't open. I had ideas on how to do this even fancier with something bolted to the frame bolts on the bed of the truck and made out of steel and even posted a couple of ideas here on the forums but others rightly pointed out I was over thinking it.
Back to your question about moving the camper, others have already given the right suggestions. I used to try to get the camper perfect on the truck through just moving the truck and would spend nearly an hour or more to get it within an 1/8". This is why I was so frustrated when my camper would shift and why I started looking for better options. When I started using the jack "crabbing" method, it saved a lot of time. Just be gentle about how much movement you try to get. A half inch to an inch is about as much flex as you will get out of the Jacks this way.
Also, depending on how your camper is loaded, you may run into the problem where it will balance on three legs while attempting to do the shift. That can put a lot of pressure on the one leg supporting the one side so be careful if this is happening and take it slow.