55.2-59 Rear axle moving left/right

[Iceman_70]

So after 11+years I finally finished the ’56…
Technical inspection is horror here in Belgium, so I now need to wait few months to get approval (or not) for the modifications I did
The license plate I got was only valid for 20days, so I drove it as much as I could . Somewhere on a stop, I noticed the rear axle moved to the left. There was like 1/8 between the tire and the fender, while on the right side almost 2”. There are some marks on the left tire, as if it was rubbing the fender…
Now that the truck is back home, I see I have 3/4 on the left and 1-1/4 on the right, so almost centered again.

My setup is :
Chevy 56 stepside, 12-bolt truck rear end with (I think) original leaf springs but I flipped the axle and the shackle hanger like it is explained here
Wheels are 18x9.5 - 6.75 backspace with 255/55R18
The space between the axle ends and the pads is the same on both sides.

I thought a setup with leaf springs is rigid enough to hold the axle centered. Or do I need to install a panhard bar/sway bar ?
Any advice is welcome !