If you hold HHonors Diamond status, there is this:

"Guaranteed Reservations availability: Reservations availability is guaranteed to Diamond VIPs when reservations are made before midnight hotel local time, 48 hours prior to intended arrival. Guarantee applies to only one room occupied by the Diamond VIP member and to reservations made with a valid credit card. Please note that this guarantee does not apply to rates - if a rate for which you are normally eligible is not available, your reservation will be subject to the hotel's prevailing rate for the accommodations requested. Please also note that in some instances, the guarantee may be subject to booking conditions such as length of stay requirements. Also note that in the event you do not arrive as scheduled and do not call to cancel and obtain a cancellation number, your credit card will be billed for one night's room and tax. Additionally, the reservations guarantee is not available during specified Extraordinary Demand Dates at certain hotels and is not available for reservations booked online. To make reservations under the Diamond VIP reservations guarantee, please contact our Diamond VIP desk at 1-877-4HHW-VIP in the U.S. and Canada. Outside the U.S. and Canada, call the Hilton Reservations Worldwide office nearest you." (HHonors membership guide.)

Unfortunately, ES near Morial fills up quickly with conventions, and the "Guaranteed Reservations" rate is not at all a low one. The only expeirnece I have had that's close to this is when I attempted to book, there were only a few smoking rooms left - by caling I was able to get that changed to the non-smoking King I wanted.