Your dates are similar to mine. The room-only discount will only cover the night of March 28. Then, as I'm sure you know, the prices shoot up to insane amounts for the next week (Easter). Unfortunately, Disney doesn't usually offer a deal for that particular week -- it used to be because they didn't need to because the resorts filled up regardless -- but the last few years the resorts have NOT filled up or even come close to filling up due to the high rack rates, so I keep hoping maybe they'll give us a little discount but I'm not expecting it. Last year I booked through Cheaptickets who thankfully did not black out Easter week and offered a 20 or 25% promo code. That is what I'm planning to do this year too....just waiting on a promo code that goes beyond March 31 so I can book the whole week.
