I don't think moving a plant would be any reason not to consider the next set of blooms as rebloom, that is what I would consider it to be.
The 'All Fired Up' never stopped blooming? So would we consider that a series of rebloom scapes or continuous rebloom? I guess the distinction would be if there was any period ( a day, a week: don't know what the time limit would be) when it was not in bloom.