Some guns are designed to be shot with the muzzle resting on the forward bag. You see this sometimes with the heavy slug guns. With full stock rifles, I find I get better accuracy if I keep the forward sandbag back near the trigger guard, or simply use my hand to hold the stock, and brace the back of my hand on the sandbag. That eliminates most if not all of the possible change in impact I will experience shooting off-hand.
Actually, years ago, I had fits trying to sight in a .30-30 rifle, with a thin, round barrel that was very whippy. It would not shoot small even groups off a rest, until I removed the forestock, the magazine tube, and spring and follower, and the two rings that held the magazine and forestock to the barrel. I loaded the gun single shot, and with open sights, fired a nice 3 shot cloverleaf group at 50 yds from the bench. I decided there was nothing wrong with the factory ammo, or the barrel, except it was too thin, and was too easily moved around by the slightest pressures. I then went about removing all binding with each part I put back on the gun, one at a time, until I had the gun put back together and still shooting respectable groups, although to a much higher point of impact.
I have used this same rest technique to test all guns, modern and BP, since, and it seems to work very well. The octagon barrels on ML rifles are much stiffer, and less prone to move around . I found an octagon barreled Winchester Model 94, in .32 Win. Spl. with a take down action, and longer barrel than found on my carbine .30-30. It shoots like a fine rifle should. :grin: