When I want to do something like this on linen, I cheat and cover it with a piece of synthetic organza in a similar colour. You can hoop it up together as a ’sandwich’ or just stitch a small piece on where you need it. The organza is sheer, so I can still see any marks or guidlines I have made beneath. Then, after I have done the stitching I cut the surplus off as close as I can get. Any threads I can’t remove barely notice. The medieval embroiderers used this technique, but they used silk gauze. I do it the cheap way!