A most excellent post^
The most forgiving springer I own is a Park 91 .177.
I hunt with springers within farmyard ranges, thats 25m or less. Most shots are standing, any support is light not the full weight.
Of a historical note, once farmyard vermin control required a solid hit with a .22. Often whatever hit hard then it was a competition between the hunter and farm dog who got there first. Iron sights were quite able to deliver a solid centre mass hit. There was no great expectation for things to be dead on impact every time, though that was an aspiration, just didn't always happen.
Once scopes with their better clearer sight picture arrived people thought they could have more range and hold tighter accuracy. Range had another 15m to 20m added and the .177 was seen as the way forward due to their inherent accuracy at these extended ranges due to their higher velocity in 12ft/lbs rifles. Thats when it was found how tricky lighter weight air rifles and their springs really were at top power shot at longer ranges. Heavier rifles became more popular: HW35E, HW77, Original 45. Expectations changed and rather than a central solid hit for a kill then head shots, very accurately placed, became and remain the shot to make.
Thankfully PCP's arrived and gave the accuracy and consistency that this higher level of precision demands. Funny, John Darling started out with a .177, went to a .22, back to a .177 and finished using a .22. Most was that he "knew" his rifles and secondly he kept his ranges moderate. Both calibres require precision, he finally arrived at .22 because he had the skill to deliver the trickier calibre.
My advice is find a shooting position that works with the rifle. Then replicate it in the field.
(I love shooting my .17HMR as the bullet is out of the barrel so fast that its difficult to do anything wrong to upset things).