RE: shrinking deer head!!!
Hotburn my Friend , what you have is an amateurish mount, whomever mounted that lacked the skills of a professional taxidermist.
The era position to the look of the face and hair tells me ,it was not tanned but dry preserve.
But now remember the skin is not the trophy but the antlers, I would get a cape from the area you shot that and have it remounted professionally , it is not everday one shoots a pretty deer.
There is not much it can be done with that head as it is shrinking and perhaps even dry rotting.
If I were closer to you , i would remount it for you at only the cost of materials.
Iam sorry my friend.