There is NOT one "correct" torque that will allow the notch to line up. There is only "too loose" and "tight enough".
Once you are "tight enough" (31 ft-lb if you want a number), you proceed to alignment. How much more torque it requires does not matter. Once you achieve "tight enough", where the barrel will not wobble in the receiver, you should remove the torque wrench and replace it with a breaker bar.
You cannot back off from 31 ft-lb to achieve alignment, as it will be too loose, the barrel will wobble in the receiver. You can only go the other way, tighter. Whatever it is, it is.
So, why does the military have the torque figure, all that jazz? Well, it's the MILITARY! They have "milspec" for everything. They probably have a milspec for how many sheets of toilet paper you can use per visit to the crapper. OK, that is an exaggeration. But I will bet they have a milspec for how many mil's thick the TP must be, and how many pieces on a roll, as well as width and length per piece. That is the way the military, and our govt does things.
OK, what about that 31 ft-lb? Well, truth be told, you could do as well with a 25 ft-lb minimum. Come on, don't tell me you never put a water pump, a starter, an alternator, or whatever on your car, without the aid of a torque wrench. Changed a tire... did you use a torque wrench? How did you know when it was tight? You could FEEL it was tight enough, right?
Same with the barrel nut. You can tell when it is tight. Nothing magic here. This ain't rocket surgery. Just get it tight enough, then advance to alignment. That's all there is to it.