I have to admit that I'm not 100% sure, but in the second case I'd disallow the run (in Fed).
Just as ASA (with its rule change a few years ago) became the only code I know that does not honor a fourth-out appeal on a runner who did not score, it is also the only code I know that determines whether an appeal of a missed base is a force out based on whether the runner is forced at the time of the appeal. In ASA, if the BR is put out, all force plays are off, period. (Exception: BR declared out for discarding helmet.)
In OBR, NCAA, and Fed baseball, for example, a successful appeal of a missed base is considered a force out if the runner was forced at the time he missed the bag. I suspect that Fed and NCAA softball would interpret this play the same way, but it's impossible to tell for certain from the rule book alone, and I don't know of any case plays to the contrary (though there may be one in Fed for all I know).
AtlUmpSteve, your reasoning certainly makes sense, but without evidence otherwise, I suspect that ASA is unique in following it.
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greymule
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