Sully, hope this response doesn't get too long. And yes, i have been listening to other points of view. With your last scenario in post directly above, the entire play is different from the original posted play. You, and others, have presented a situation where the batter-runner passes the preceding runner BEFORE the ball goes out of the field of play which would result in this call.
Loudly the umpire declares "Batter-Runner is out for passing preceding runner, 3rd out, game over. Supported by this rule that i had listed earlier in this thread : Rule 5 - The Game, Section 5 - Scoring of Runs, Para B - NO run shall be scored if the third out of the inning is the result of: 2 - A runner being put out by a tag, called out for passing a runner or a live ball appeal prior to the lead runner touching home plate.
I have just been advocating that the way the original scenario was posted, ie "Ground rule double has already been declared before any of the other action occurs (please go back and read the OP), the plate umpire would loudly declare, in order, 1) ground rule double 2) dead ball 3) all runners awarded two bases from original position at time of pitch and this would be the rule in effect. And of course, the runners would have to complete the direction of the home plate umpire properly or be in jeopardy of being called out. The umpire is the director of the play just like in a movie. Not being argumentative, just trying to follow the timing of the original play and apply what i deem to be the correct ruling as written in the rule book. My ruling would be exactly as i have stated above, again depending on what i would see from home plate in the timing sequences posed above. One ruling from the original post, a different ruling from your proposed timed play.