SKN, your step two is how/why people miss running deer and doves.
It takes practice. The idea was told to me by Chip McCormick, and when somebody of his expertise speaks, I listen! What was new to me was the application to pistol shooting; the actual method is the way I'd been killing deer, doves, rabbits, quail, etc., for decades...
Basically, you're increasing pressure on the trigger as you sweep; just before the front sight bears, you tell your trigger-finger to do its thing; when the gun actually fires, the sights are dead-on on the target--and you keep sweeping toward the next target.
At an IPSC or IDPA match, *listen* to the top shooters as they shoot multiple targets. For the best ones, the sound of the gun is a fairly steady beat, or pair of beats for "double-taps".
Say you have a crossing dove. You bring up the gun, catch up to the dove and pass him and hold the lead--continuing the swing, right? Your gun is moving while you shoot, and you keep moving in the traditional "follow through" due to the discrete time-lapse between pulling the trigger and the shot exiting the barrel. If there is a second bird, you continue moving and repeat the process.
Hope this is a bit more clear,