So, take it easy and really play around until you find a way to shoot this thing.
Thanks for the breakdown. I agree that it is likely to be technique, coupled with inexperience in what to expect.
The first time I shot it, was the first time I had shot a centrefire rifle. My sight height was wrong (as I now understand), I was shooting from a bench rest because my barrel control is so bad at the moment and the stock had a granite shoulder plate.
All those factors added up to my first .308 experience being stouter than it might have been. Having said that, a .308 is a powerful round in its own right, despite some of the manly-man-man remarks. It may not come high in the recoil league tables, but that doesn't mean it has none!!
Besides... I have muscles! It's just that a fair proportion have migrated to my waist....
I have since replaced that shoulder plate with a rubber recoil pad, I have moved to a more upright seated position, and replaced the scope with a model of greater eye-relief. I now only need to address the sight height issue.
Already the recoil is more of a shove than a punch.
I will soon make a stock block to raise my cheek, up to the level of the scope and I will try and visualise my shoulder position to match your suggestions, so thanks again!