I can maintain the sight picture off the shoulder as you state with a 270 Sako bolt I shoot but don't maintain that well with calibers above that.

I feel sure if I compared the quality and speed of shooting the same caliber Double by maintaining the grip then while going for the 2nd trigger vs the same caliber bolt the Double would be a faster and more stable shooting platform for me. Your right hand movements are far more complex at speed with a bolt-- releasing the grip, wracking the bolt and then attempting to get a decent grip and trigger position at speed.

Now if I could just afford a small caliber double with a scope----

Foxfire--
Betcha most american hunters erronously consider all cailber Doubles only fit for short range game and feel that their bolt rifle is much superior to any small cailber Double!!!