I can't substantiate all of this, but I assumed that it would sell out very quickly so I woke up at 5am the day of to book it (July 23rd Cruise from Liverpool), and I believe it sold out that morning. Disney did a very poor job in this regard imo, as "broadway style shows" are a main selling point of their cruises, especially in a cruise where many normal activities have been cancelled.
HOWEVER - as of today, 5 days from sailing, there appears to now be availability for the late showing on day 2 (obviously I can't book it because you are only allowed to book it once and my wife are already booked to see the early showing on day 4. So it's possible that they add more shows once they see what the crowds are like.
I do completely understand and side with your frustration. Now, one the earlier Liverpool sailings (15th, 18th), I heard they added a Matinee show to cater for people who missed out, so it's possible that will happen on your cruise too, but that was only something someone posted on Facebook.
Good luck!
P.S. The two times I contacted
DCL on the phone they were very helpful, they might know more. Failing that, you can always check with Guest Relations when you got on board for any last-minute availability.