Hey there, Coypu Hunter .. I was in the same boat mate, got a hw97 after a few years off shooting, and thought 2p sized groups at 35 yards were as good as it gets.. then I seen verminhuntersTV and the accuracy they were getting, I thought only pcp's could be that accurate. then I kept practicing. a hell of a lot! and now my groups are almost always 5p sized rather than 2p sized!
so practice really does help. lots of it. practice practice pactice my friend!!
as for the tune making a rifle more accurate, nope. they are built to be accurate, its just easier to get the accuracy if there smoother to shoot.
my reccomendations for pellets would be JSB exact , mine loved 4.51 and 4.52 about the same. and my 95k loved these aswel, now that was a hold sensitive rifle!!
as for getting all anal and weighing your pellets into batches of 8.7 8.8 etc, go for it, when your b ored on a rainy night infront of the tv lol
at 35-40 yards it really isn't neccisary, but at longer ranges you may see a slight difference. I don't bother personally.
as for head position/eye alignment, I don't know what scope you use but the panorama ev I have on my hw100 has a very 'fine' eye relief, what I mean by this is my eye has to be in almost the exact same position to get a sight picture, this helps in knowing your holding the rifle the same. some cheaper scopes you can look through them from 8 inches away or 2 inches away and get a good sight picture (slight exaggeration lol)
with my hw97 I hold the very end of the stock, I place my thumb lightly in one stock screw hole, and my middle finger in the other, my index finger is at the left side of the front end of the stock. then I know my right hand is in the same position shot after shot, lightly cradling the rifle as you described.
with the hw 100kt I have my trigger finger rested just touching the bottom inside of the trigger guard so I know im pulling it (squeezing it really) exactly the same everytime.
its all these little things I do that make sure im consistently holding the rifle (cradling it) every time and I think this has helped massively in my own mind to get better results, I see it as a way of ticking off the list of variables every time I shoot the rifle! I do still focus on them , just in the back of my mind so I can concentrate more on the other stuff like how loose/tight my 'grip points' are on the rifle so I can focus on balancing the pressure out equally.
anyway I have rambled long enough!
just get out and practice and enjoy it im sure you will start to see better results soon mate, took me a good year but when I took out an old target card to compare after 1 year the results spoke for themselves! practice makes perfect.
happy shooting mate
1 shot SKoT