[officialtony]

Why is he carrying the bat so far up the baseline?
Most of the time ( not always! ) that bat is dropped or tossed very close to home plate or the dugout, particularly if the batter thinks he is out - or will be.
With the bat in hand that far and then suddenly tossd where the play is happening . . . . . . . . . . . . . . I am going for batter interference.
As far as I am concerned, based on your description of how it developed, you nailed it.