And you could also check for dust in the pivot point, that sometimes helps...
Oh! I see that you mention having done that already! My bust
...
I placed my scale on a piece of glass, and I make sure to keep the glass slab clean.
What I think you're going to find is foot movement on the scale. The little adjustable foot that screws in and out has a wobble to it. Each time you touch the scale, this foot wobbles in the threads, and changes the zero just a bit.
After you make a level base for the scale (out of a piece of glass or marble tile, etc.) you can then take a lock nut of the thread size that the adjustment foot uses, zero the scale, and lock the nut down.
Also keep in mind that the farther you screw the foot out, the more wobble room there will be. It may help to place a small glass piece under the foot so that you don't have to go out so far with it...
Another idea: Take a strong rubber band and hook it over the adjustment foot shaft, and wrap the other end around the main body of the scale. This will keep the foot in the same position...
Let us know what you find...
Dan