If you really want to eliminate most of the human error, there is no substitute for a solid pedestal front rest and a rear bag. Bipods can work but technique is very important- the way you "load" them can have a great effect on elevation.
This is my son's partner (no, she's not available..) shooting with a joystick front rest.
You don't have to pinch the rear bag to get the final aim. Even with this rock solid setup, technique is still very important. Variable shoulder pressure / position, cheek pressure and trigger technique all affect where the shot goes
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