Wow, I just posted this last night super late — and so many of your already responded! THANK YOU!
I'll address the responses and suggestions here in summary form.
Those where I have follow-up questions or that I will need to try yet are marked with an
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(1) Check the barrel: ➔
I'll make a separate post about that. ➔ Note that the Skyhawk was sold to me with a barrel upgrade to a Lothar Walter drop-in barrel, from JSAR. And that I tried not one but two .22 barrels in the PP700.
(2) Ask someone to shoot a gun of theirs that has a proven precision. ➔ Yeah, that would show how bad I really am...! Good idea. But... — I just don't know any AG shooter here in Peru.
Time to make some friends, I guess.
(3) Buy a full auto LCS SK19 and all this will not matter anymore. ➔ THAT, my friend, is a GREAT idea.
If someone will present me please with the second GREAT idea necessary to make this work — I'm all ears:
How can I convince my wife to spend that kind of money? (4) Be careful to follow-through with each shot. Vetmx wrote: "What’s your gun doing when that trigger breaks and the gun goes off? This is where we all make mistakes because we are just so excited to shoot and don’t take the time to get everything just right.
"If you are in the bags right, if the pressure you are exerting on your gun is just right, when that shot breaks your scope picture will look the same every time.
"If one shot your crosshairs jump to the left of the bull then your next shot jumps to the right, you are going to struggle at 100y with an airgun. It’s because the shot process is so slow compared to a firearm. It just takes way too long for a projectile to leave the gun after you squeeze the trigger on an airgun. This amplifies all the little things we do wrong."
➔ I think here is something I can improve on — I noticed the difference when hunting pigeons — more DRTs when I remembered the follow-through.
(5) Questions about the gun rests I use: ➔ Skyhawk: Front = bipod, swivel and tilt unlocked | Rear = sock with light and very smooth plastic chips (very soft)
Bench = sturdy folding table (yes, not made from cement like some benches....) ——
Would that make such a big difference?
➔ PP700: Front = sock with plastic chips | Rear = same.
Though sometime I only use a folded towel for either front or rear. ——
Would that make such a big difference?
Bench = wood board on crates
(6) Have a good shooter try your guns. ➔ I don't know any in Peru....
➔
Maybe it's time to make some airgunning friends!
But a bit complicated with an extremely strict corona lock-down in Peru.
(7) On the forums it is common to post 5-shot group. You shoot 10-shot groups — so comparing 5-shot to 10-shot groups is skewed. jiikuu wrote: "Thats the smallest acceptable ammount of shots to meassure accuracy."
➔ Yeah, I learned that from Ballistipedia.com — and decided against the 5-shot groups. (Well, 3 or 4 groups of 5 shots would also be statistially sound.)
(8) Try a Mantis X2 sensor on the gun to examine your shooting errors: https://mantisx.com ➔ Entry level $100. Live fire version X3 $170.
Interesting option. I'll check that out.
(9) To evaluate groups correctly they should be somewhat evenly spaced out (or "normally distributed"). ➔ Yes, my groups are usually that way. I actually discount the flyers at 100y when there are 1 or 2 shots that are 2-3 inches away from all the others. But not even that way I get near the precision I read about.
(10) Check with a gun vice. ➔ Interesting. I don't supposed they sell those in Peru. I'll keep that in mind for my next US order.
(11) Use slightly different velocities. ➔ Skyhawk: So far I tried 3 power settings (in FPE, for the JSB Domed 16gr): 30, 29, 26.5
➔ PP700: So far I tried 3 power settings (in FPE, for JSB 14.3 and/or H&N 14gr): 15, 14.3, 12
(12) Attempt to shoot ragged holes at 20y before attempting groups at 50y. ➔ Not sure I'd be happy shooting at 20y — though the pest animals would be very happy if they are safe from my shots beyond 20y....
I understand that wind and ballistics will open groups up exponentially, so getting 1" at 50y will not guarantee 2" at 100y.
However, (a) I'm trying to shoot things/ pests at longer ranges and (b) I'm comparing my results with results I find on the forums — and there is a huge gap. That's what got me writing this post in the first place....
(13) Sort and weigh and lube the pellets. ➔ I almost always buy only high quality brand pellets (JSB, H&N).
And if I was trying to shrink a 1" group at 100y down to 3/4" — I might sort and weigh. But I'm stuck at 3" groups....
And it seems there are top level competitors that get away without all that....
Just saying.
(14) Clean your barrel. ➔ I thought I could get by without that — there are some very good shooters and AG nuts who say it's not necessary (except for the peace of mind of the shooter).
Well, I finally buckled under the disappointment of my shooting results and bought a Patchworm kit. Nice kit.
However, the results after 3 ballistol patches and 4 dry were not really any better.
(15) Switch the PP700 from .22cal to .177. ➔ I kind of like .22 — and would making better groups really require a change as drastic as changing caliber?
I did consider getting the PP700 in .177 — but the pellets are so tiny, their BC so poor, and buying another whole set of ammo....? I'm desperate, just not quite that desperate yet.
THANKS A LOT for all your help!!
Matthias
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(1) Check the barrel: 
