FWIW, I used this with an Agfa-Ansco that had a wooden track, so YMMV on metal-to-metal tracks. I cut strips from the thickness that seemed to give a tighter fit without binding, somethingwhich would vary camera to camera, hence getting a pack with varying thickness brass sheets. It doesn't take a lot of slack to result in discernible wobble on a high-leverage situation like an 8x10 back.
I cut strips such that they would fit the width of the slider top, but not more, and not bind . These would be long enough that the front and back could be wrapped beneath the front and back of the slider sufficiently to provide some tensile strength. A very thin layer of good adhesive was applied to the parts wrapped around the bottom part of the slider.
I suggest first experimenting with no adhesive to find the correct thickness and then with an adhesive that can easily removed in case this workaround is insufficient to solve the wobbling or needs to be replaced.
As I have not used a Kodak 8x10, I don't if there is a spring-loaded or similar mechanism that Kodak uses to tension the track to slider contact? If so, I would first look there to ensure that any tensioning mechanism and any lock-down mechanisms are working properly before modifying the slider.
Before trying home-brew approaches, why not first take this to a competent machinist and see what sort of fix the machinist recommends. I've found that to be optimum.