Here's how I do it/did it whatever. There's nothing much to process....
I don't use a front stop. They cause problems such as Markhor is having. If he tossed that front stop he could push the rifle further forward and eliminate his problem - but I digress.
Not using a front stop I fire a shot, reload, put my left hand on the rear bag, look through the scope and as I'm pushing the rifle forward the crosshair magically goes straight to where I want to aim. When it gets there, I pull the trigger and repeat three more times for a total of five shots. Actually, the first shot doesn't take any of your 15 seconds so that leaves 3.75 seconds per shot.
About that magical crosshair travel...that comes from hand eye coordination developed over a bazillion shots. As I push the rifle forward, my left had moves/squeezes/nudges the rear bag left or right as necessary. I don't even know how it does it - it just does. Without the front stop the vertical component is adjusted with my right hand (rifle position) without any thought on my part.
When you "run 'em" you glance at the flags while loading in an attempt to detect a change such that you need to stop. Any more than a glance and you should stop anyway because you are no longer running. Basically it's a suicide mission that very often ends with a really good target. Once burned (usually pretty bad) a competitor is reluctant to try it again but here's another question to ponder. Would you prefer to win every now and then or lose every time just because you don't want to get burned?
Alternatively, you can watch the flags carefully, make sure that you and your rifle is in the exact same position for every shot and shoot when the flags are the same for every shot. I wish you good luck with that approach. All too often you'll find yourself in quite a pickle at the one minute warning and get burned. Of course, that doesn't count as getting burned because you were trying to do it "right" - a victim of circumstances so to speak.
Tony Boyer said, "The most important decision you make is when to start your group." It follows that if you're not gonna shoot your shots right then and there you can start just anytime you like.