I hope you understand that whatever you do, the patches will show to some degree. I think I would use epoxy. Fill the holes and let it dry. There will be a bit of a bump and the color won't be a perfect match, but I really don't think there's much more you can do. If you have friends who will inspect your bathtub and pass the word around your neighborhood that you have patches that show on the edge of your bathtub, you need some new friends!
