Pearl Harbor, Diamond Head, and Hanauma Bay are best done early in the morning. You may not be visiting these places with young kids but if you were planning to, I'd schedule them at the start of your trip. We also did a 9am tour at Kualoa Ranch, which required us to be there at 8:15 for check-in. Because of the travel distance and traffic, we left Aulani at 6:45 which worked out just right, so that might be another option. Dole Plantation is also best done when they open, which I believe is 9:30. I would give about 45 minutes to an hour to get there during rush hour.
We also had a 6 hour time difference adjustment. Our first night, we were out by 8pm and wide awake by 5am the next morning. It got a little easier each day, and I'd say we were fully adjusted by day 3. We stayed in Waikiki during our first few days, so there were lots of options for walking around, grabbing coffee, etc. A lot of others were out and about that early, likely in the same time change boat as us. Aulani doesn't seem to have as many options for things to do or see at the resort at that time. I don't know what time the pool opens, but I know you have to be with your stuff at the pool before 8am or risk having it removed - so maybe 8am?