Hm. What I'm getting from Bob's (as usual) superb writeup is that we wait for either an appeal or a play on the B/R for failing to complete his advance. In our OP (unlike Bob's) a successful appeal will nullify the run and start extra innings. But how long do you wait?
I guess until the runner enters DBT or other circumstances end any chance for appeal (defense leaves infield, etc). A rather unsatisfying answer, to my small mind.
I don't understand your angst, JM. You can't really be serious that you would not appeal a decision that would save a loss and send your team into extras? They are going to rescind your Cheese Eaters' Club card any day now