Is a gross miss correctable?

[greymule]

Just got Rick Roder's 100 Problems with the Official Baseball Rules. What a terrific book. Not that too many of these plays are likely to come up in tomorrow's game, but the situations are certainly thought-provoking.

In reviewing one play that I was familiar with, I have begun to wonder at what point a runner who has committed a gross miss of a base cannot correct his mistake.

The generic play is this:

Abel on 1B. Hit and run. Baker hits a liner to right center. Abel rounds 2B and is halfway to 3B when F9 makes a diving catch. Abel, instead of retracing his steps toward 2B, runs across the diamond directly to 1B. F9's throw to 1B goes into DBT. Umpire awards Abel 3B. Abel tags 1B and then 2B on his way to 3B.

Because Abel's miss of 2B was "gross" (more than a body length), the umpire should uphold an appeal of Abel's miss of 2B in his attempt to return to 1B. If the miss had not been by more than a body length, the umpire should not uphold an appeal, since Abel touched 2B "the last time by" when he took his award.

But I'm not sure how to rule on the following plays:

Same situation, but—

A. Abel cuts across the diamond and is approaching 1B when he sees F9's throw go out of play. So instead of touching 1B, Abel runs directly to 2B, then retags 1B and proceeds to touch 2B again on his way to 3B.

Should the umpire uphold an appeal for Abel's gross miss of 2B, or did Abel, in his roundabout way, correct his error?

B. Abel cuts across the diamond and slides into 1B. The throw then goes out of play. Abel then runs to 2B (to correct his error), retreats to 1B, and then proceeds to 2B and 3B on the award.

Did Abel properly correct his gross error, or is he liable to be called out on appeal?

C. Abel cuts across the diamond and sees F9's throw go into DBT. Abel then touches 1B, runs to 2B to correct his error, retreats to 1B, and then takes 2B and 3B on his award.

Should the umpire uphold an appeal at 2B for the gross miss? Did the fact that Abel proceeded to touch 1B after the ball became dead affect his attempt to correct his error?