Yes, you are kidding yourself and it will be busy.
April 27th is the last day for the kids fly/ play free special. The trip doesn't have to be over by then, it just has to be started.
It is also the last day that the S. CA 2fer passes are good. People that have put off using their pass will be there.
The 27th is also the date trips need to be completed by, to get a $150 gift card for a 4 night stay on site.
If you must go that week, go after the 27th!