Look for reservations closer to the end of your trip! Make sure that you're up early on your ADR day (we did 5:30-5:45 a.m ET to get set up and had all of our restaurant pages open in separate tabs. That way, when we logged in, we just had to refresh each page) and have that be the first one you go for. We booked in August and we were able to snag ours at about 6:15 a.m (it wasn't initially on our list and we decided on the fly that we wanted to try it)...and granted, that was a much lower crowd time, so I wouldn't recommend waiting if it's an absolute must-do.
One other thing that we did ahead of time was sort of play with the dining availability in the app. So I'd go in, select the furthest day you could go for and see what came up as a way to sort of gauge what restaurants might be a little more difficult to get.
Good luck!!