Have you tried to reset the Axis orientation?
Maybe if you do that, so that the lower side of the cap is then set as the ground plane (x/y plane), the plugin might then lay in the stitching to your liking.
On a positive side here… now that you’re dealing with edges and faces, there might be something to be said for using the push/pull tool to add some thickness to your stitching. That would certainly help create a nice decorative topstitch look. though it’s gained at the expense of increasing the edge and face counts in your model.