Grad Nights aren't too horrible, and I think the ones in early May are the least crowded. The parties take place at DCA, which usually closes earlier than
Disneyland anyway. The grads do have access to both parks during the day, but they have to arrive as a school and many schools have a long drive to get there. The biggest thing that guests complain about is language of the grads. We haven't experienced anything worse than we would on any given day, so I think it depends on the groups you run into.
The early closures is something new to me. I wouldn't be surprised if they're actually CM previews of the 60th entertainment. Disney certainly owes it to the CM. I'm really hoping for my AP anniversary party the week of the 17th of May, as that's when we'll be there and there is only 1 grad night scheduled, so they have time

.
I would say use your early entry privileges for staying at the Grand and get to the parks early. Come up with a plan. Know which park you have early entry to and which park closes early (Disneyland for private event or DCA for grad night). Decide when you're going to visit each park, and make sure you park hop. I think you'll be fine as long as you're aware of how to use your early entry and which parks are closing when. Also, take a look at TouringPlans.com your days are currently on their free preview. They'll give you an idea of how long the lines will be for various rides during your trip.
As far as the parades a few people mentioned, entertainment schedules are always posted a few weeks after the hours are posted. No Fantasmic in midweek May, but there should be a parade.