The only thing you can do in this isntance is add a little noise to the image. This stops the stepped-gradient effect happening when you start adjusting things. The noise can then mostly be removed afterwards.
It isn’t perfect, but can stop colour banding from occuring when manipulating 8 bit files.
This was my first solution in the tool as well. Currently, I’m using a different approach, where a smoothing parameter is used to decide the smoothness of the gradient. This reduces stair stepping and similar artifacts.