Just a tip for the first week of May that people are having trouble with. We tried to book then, too (on a different offer) and were also denied, but one of the reservation people we talked to told us that there's a convention booked there and they have a ton of rooms blocked off right now. She said that it's possible that some of those rooms may get released as the date gets closer, so it may be worth it to call and try again in a week or two -- the date you need may open up.