What kind of egg is this Charwolf? It is a beautiful color.
What day is this egg at incubation wise?
You said it has been 36 to 40 hours from the initial external pip? That purple area concerns me. I think it looks like blood. But if you say it is tapping in the opposite direction and that membrane is dry and white. You can try to gently just remove break the shell a little at a time and slowly peel the membrane in that are if it looks dry. Hopefully, you will free him enough he can push the rest of the way out. Or Maybe it was / is in a bad position? And will not be able to make any more progress without help. I just really don't know. Maybe go with your gut!