I just booked my ADR's for June using the new dining system. I started calling at 6:58am, and once the line opened, I was placed in the hold que for approximately 40 minutes. How it is working now is that you give the reservation agent a "time frame" that you are wanting to dine at a particular restaurant. Then they see what's available. You are no longer given a confirmation number at the end of each ADR. All reservations are placed in a "shopping cart" and when you are done, you give the agent your credit card information, if necessary for some ADR's, and he/she re-confirms each ADR and provides each confirmation number. The numbers are now 12-digits long, so be prepared to write. Also, make sure that you have your hotel reservation number available. You cannot begin the ADR process until they have it. It is the first thing they ask for.
Hope this helps all who are about to make "the call".

P.S. I was able to get all of my ADR's. WOOHOO