Elsewhere I have brought out the point that the use of a .45 calibre bullet is not overkill merely because a .22 calibre bullet would have also been sufficient.One massive blow is not necessarily overkill. A dozen such blows would clearly be overkill indicate rage, frenzy and contempt.
The injury was severe, the blow was probably unnecessary due to the effects of the strangulation, but it was not necessarily 'overkill'.