Interesting, Steve. I found my .40, a 1/2 stock, required when shooting chunk, that the barrel had to be rested on a bag just behind the second pipe- or just behind the entry pipe. Either position gave it exactly the same group size, although the further down the barrel resting, elevated the gorup about 1/2".
I haven't tried any of this current lot of guns off cross sticks, except for my .69 and I do not let it have it's head. I hold on to it's stock as if shooting offhand. That way, the poi does not change and I can control it's climb, somewhat. The gun's rise on recoil is bad enough when holding onto the forend. I don' t want to get smacked in the beak by the hammer or barrel for that matter, by letting it get a running jump.