Answer to Daryl and Beleg2 (as they both might pertain to stance):

Daryl, the reason why you might get different results with shooting your guns on a rest, versus your hands on a rest, (I assume you are standing in both cases), might be because you unconsciously assume a different stance when you shoot what you call benchrest style: The 1' to the right and 3' inches high relative to POI sounds familiar to me, as I kept getting this result consistently when first shooting my double, irrespective of whether I used a rest or not.

Well, in the very beginning I was shooting .470 factory ammunition over my Africa sticks and assumed a completely square stance doing that, which I then also used for shooting off-hand. The strange change in POI puzzled me, as regulation pertaining to tight groupings was perfect, and as I doubted that the iron sights were misaligned by Holland & Holland. For a while I thought this might be a result of the sun hitting the iron sights in a bad angle as I was usually shooting outdoors in the same spot around the same time. It was the same in the shooting range however, and I had already considered changing the sights.

Well, after a while I started reloading for my double, and as I like powerful loads I concocted some which approach a .500 NE in energy levels. Of course, the recoil went up as well, and my square stance was so unstable in regard to those loads that the recoil almost put me on the floor. So I changed my stance to completely sideways - and guess what, I was shooting low and to the left (also with the factory ammunition). It took me while to actually figure out what the reason for those changes in POI really was and to find the stance that worked with my gun. Let me just say that I now shoot with a half-open stance (similar to shotgun / Weaver stance) and my POI is right where it should be - square on where I aim.

So, for everyone who is puzzled with an incorrect POI, while otherwise shooting tight, well-regulated groups, it might be a good idea to open / close the stance to see whether that might make a difference. And as Daryl rightly commented, a 'hard' grip will have some influence as well. If the gun was regulated with a hard grip, then it might quite possibly be necessary to replicate that hard grip. For my Holland & Holland, a 'soft' grip and a half-open stance were right on the money, for other guns that might be different. So Daryl's observed difference in regulation when shooting off a rest relative to holding the gun on the rest might not be the fault of the rest (or an incorrect stance), but the fact that his gun needs a hard grip, irregardless of what it is resting on.