Some more discussion before we declare the horse dead and stop beating it.
As many have pointed out the time to decide where to protect an obstructed runner or batter/runner is at the time of the obstruction.. But I think some people are taking that to mean a snap decision the instant you give the DDB signal. IMO it means making the decision based on the events at that time and nothing else. The only thing you are communicating immediately is that you saw the obstruction.
So batter gets base hit to outfield. Bumps into F3 rounding 1B because F3 has become a spectator. Umpire gives DDB and states "Obstruction". Now it's time to decide how far tot protect.. But the umpire can certainly take enough time to see where that batted ball ends up before deciding if it was a double or a triple.
You can take this time because your still using the action taking place
at the time of the obstruction to make your determination of where to protect i.e. The BR was obstructed while running on a batted ball, and that batted ball is still rolling around for some time after the obstruction. By the time defense corrals this ball and throws it in you should have all the info needed to make a judgement call: that hit was a single/double/triple. After that no more changing if obstructed runner tries to stretch beyond the protection and is thrown out, even on a close play it's still an out. By the time a play is made on an obstructed runner the decision on where to protect should already be made. And if obstructed runner stops at a previous base then at end of play umpire should award her the base protected to.
But think about this: the rarest hit is a true inside-the-park home run followed by a true triple. To protect this batter-runner to 3B she had to be able to get there without benefit of a fielders choice elsewhere or a bad throw etc etc.