Screw that - head shooting a sitting bird with a shotgun is the way to go.... KISS.
If it is good enough for turkey hunters, it's damned well good enough for grouse!
Once "head shot" a ptarmigan at about 15 feet with the scope-sighted '06 while sheep hunting. Forgot the scope is a mite higher than the bore.
Wound up with the head and the back skin all the way back to a single leg, plus a smear on the rocks.