Actually, I have found that arriving at night sometimes helps with the upgrades. I have been upgraded PLENTY of times at the HRH. From standard to pool view, from regular room to deluxe, from standard to club floor. At 10 p.m. they have a really good idea that they are not going to "sell" the room and will more likely give it to you. If you checked in at 10 a.m. they would be hesitant to give it away for a few reasons 1. not everyone is checked out and thus they might not even know how many vacancies they have 2. Hoping to upsell a room 3. hotel overbooked and they are waiting for everyone to show and have not had last minute changes and cancellations.
Also, for suite upgrades ($35) they will most definately be more open to doing the upgrade later in the day. Ask if any are available. We got upgraded to a kid suite this way. It was great.
I have found the HRH desk to be really friendly and helpful. Have fun.