MeshCAM is not the right software imo (and I'm a MeshCAM user.) Personally, I wouldn't use Sketchup either, due to it's lack of arcs.
Normally, inlays are done with a 2D drawing and a 2D CAM package.
In a 2D CAM package, you'd want to cut a pocket, and most 2D CAM programs have an allowance to let you adjust the pocket size. Alternatively, a 2D CAM program will let you easily offset the outline of the pocket by the desired clearance amount.
If you must use MeshCAM, have you tried to use a Pencil Toolpath to follow your grooves more precisely?
Or, you can Tell MeshCAM you're using a slightly smaller tool, and it will cut a little larger when you use the actual tool.