OK I know something about this? I use the "Artillery Hold" to Sight In my Springers. I have a 6x6 that is 2 feet long sitting on the end of my Reloading Bench. It is inline with the guns and the target in my shop. I have a Bath Towel on top of it and the guns (HW35's 77 and R1) easily slide on it and it doesn't affect the finish at all.
The guns line up with the targets close enough that I don't have to jack them around to hit the same spot every time. I have both hands on the gun but the strong hand is only grasping the grip with the Heel of my Hand and the 3 lower fingers have the last pads on the front edge of the grip. Trigger Finger is completely free to caress the trigger. (Rekord Triggers are among the best there is!) My shoulder is on the gun but there is not any pressure drawing it in, it is more or less just resting on my tee shirt. Support Hand is laying next to the fore end not doing much at all.
As the shot breaks the gun is free to move about 1/4" back and that is all that is needed. The gun moves strait back and the pellet is already gone in the first few Milliseconds. It's like "Following Thru," except it is done for you by the set up.
In Field positions IE; Off Hand, the gun is supported by my Support Arm carrying most of the weight and pulled into the Shoulder Pocket by the Firing Hand. Cheek Weld must be in place for Iron Sights as that is the only way you can get Repeatable Sight Alignment . When using Open Sights you lock in the Front and Rear Sight Alignment with your Cheek Weld and then put the Front Sight on the target and fire. Then you are concentrating on the Front Sight only as opposed to shifting focus back and forth during the shot like we all did when we were kids and had perfect eyesight.
With Aperture Sights, since the centering of the Front Sight in the Aperture is automatically done by your eye, you only have to worry about your Sight Picture. Put the Front Sight on the Target, or more properly try to duplicate the "Sight Picture" that results in a hit, and let fly... All this takes practice, and that's why you bought an airgun in the first place,,, So you could shoot more and get better at it!.
One other thing you can do to improve your shooting is using a Diamond Shaped Target Spot and use the bottom point to index your Front Sight or Cross Hairs on. A friend of mine who writes for Handloader and Rifle Magazines told me about how he and his sons shoot more in one week working up loads for an article, than most of us will shoot in a year, or in some cases a lifetime! His Test groups are always impressive, but it's not because of the loads, it's because of how they index the Front Sights on their targets. What this does for them is give them an easily "Repeatable POA," to index on and almost eliminate the Shooter from the Accuracy Equation. Thus it becomes possible to actually be able to figure out which loads perform best in each gun. This would work for Pellet selection as well.
When I see pictures of Generic Leverguns shooting Sub MOA Groups with Iron Sights with many different loads I can see there is some skill there to pay attention to. I have been doing this for about 10 years now and it works,,, trust me on this.
Hope some of this helps in your Quest for Airgun Nirvana.
Randy