JRoe
To remove the bad influences of the human element without resorting to uber-sophisticated & expensive shooting rest /clamp devices, probably the most effective aid is to make the firer comfortable & ergonomically right. i.e. use proper profiled shooting bench with a comfy adjustable seat set at the right height for it. You can't shoot well repeatedly if you're uncomfortable. A prone position can help if there isn't a good bench around & it's particularly good if you can lie without needing to strain upwards to get on target i.e it's nicer to shoot down hill from a flat bed than up hill.
Then bunny bag rear (set at the right height) & a solidly built, adjustable front rest or bag rest set at the right height will work in your favour. I often use elbow pads to reduce discomfort too. (I used to get skinned elbows when I did some long load testing days on the benches at the BSRC Bisley).
Whatever rests you use they should be firm, probably quite heavy yet soft surfaced to aid comfort.
If you want to play, I have an adjustable front rest you can borrow to try.
Ian