My $.02. The experiment is not very convicing. It may look good on the surface, but not when you dig deeper.
The situation is somewhat like this. Suppose I claim that I have a psychic that can receive "information" faster than light. And I have an experimental result that supports this. The experiment runs as follows:
We have a mechanism that generates the following numbers - it's not random, it's a pre-recorded message. It goes something like this:
1,2,3,4,5,6,7,8,9,10,11,12
We send the first 12 numbers in the sequence, and we ask the psychic to predict the next number in the sequence before it arrives. The psychic, based on the information that was received, correctly predicts that the next number in the sequence is 13.
Have we convicingly experimentally demonstrated the transmission of "information" faster than light by psychic means? I would say that we have not.
How does this analogy relate to the experiment? - Mozart is music, which is a strictly band-limited signal. The propagation delays being measured are on the orders of fractions of nanoseconds (less, actually). On this scale, Mozart looks essentially flat, because the highest frequency in music is 20 khz. 20 khz * 1 ns is 20 / 1,000,000 of a cycle. Over an interval of such a short duration, sines and cosines look essentially flat.
To be convicing, a much wider bandwidth signal would need to be sent, or a much larger timespan than a few nanoseconds would need to be used if one insists on using Mozart.