Deer stalking expert
Im tempted to say it serves you right for reading other shooting magazines but I shall stay my hand and try to answer your question sensibly.
Overkill means causing a great deal of collateral damage when, for example, an airstrike is called in to wipe out a village because there is a sniper in the church tower.
When it comes to shooting an individual animal, dead is dead and thats the end of it.
If you suspect that the .308 might smash a lot of meat, let me set your mind at rest.
Some years ago I was lent a Lakelander rifle (one of the best production rifles I have ever handled) in .308 and we shot everything with it from Red to Muntjac.
I well remember BASCs then Head of Education shooting a Muntjac end-on (from in front, of course), and finding the bullet in the haunch as he was carving the family dinner.
There was absolutely no meat damage.
The bullet was a nice, round nose 180 grain and it had done no harm to the deers flesh at all.
Apart from sudden death, of course.
I leave you to draw your own conclusions and wonder, perhaps, whether the use of a smaller, higher velocity round such as the .243 would have produced such a happy result.