BZ, a carry that is followed by a dribble IS a special case of an illegal/double dribble because the dribble ended on the carry and another was started. If at the point that it would have been a carry, the player, instead, did not push the ball back to the floor, it would be perfectly legal....because the player has caught the ball. Anything after is a new dribble. Note that the case you cite says "ATTEMPT" to continue the dribbler. However, the attempt is not permitted since it would be a new dribble.
This notion is supported by the fact that they removed the carry signal a few years ago and let the violation be either traveling or an illegal (double) dribble. They only put it back because it was confusing...not because of a rule change.
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