Is there a formula where I can enter in X Y and Z to get the amount of um the rail should travel between each shot so I only slightly overlap for each depth of field slice?
Since a rail moves the entire camera forward or backward without changing the focussed distance, you just need to know what distance you want between shots. If you know how much total depth of field you're getting with each shot, you'll probably want to make your layers bit less than that. Using a depth of field calculator can help, although your macro rings may complicate that.
Here's an example: Using a 60mm lens on a full frame Canon 5D, and a distance to subject of 20cm, f/4 gives you a depth of field of 0.19cm. So you might want to space your layers around 0.1cm.