Actually I kindof did it with your original file, but mechanically I think it is slightly off. I used one of the curved surfaces of the slider area and projected a line onto it. The I created a circle from 3 points with that projected curve to re-create the arc needed. Here is the file that "looks" like it slides, though I think to be exact, you should do this an keep the original cutting arc in place to use as the center of rotation to have it be proper!

Anyway, maybe this gives a better idea.