Couch,
This is my first post but I have summited Whitney three times in the past five years. With plans on an October summit this year. Staying in Mammoth is a great idea. I do not think it is necessary to stay at the Mammoth Mountain Inn. The Inn gets a load of bused in tourist each night. The rooms tend to be warm and the mountain lacks decent dining. You can also book a condo in town for the cost of a room at the Inn as well.
For acclimating hikes, I prefer Little Lakes Valley. The trailhead starts at 10K, the valley is beautiful and the trail is really nice. Also, Virginia Lake is fairly high with nice trails too. In Mammoth go up to George lake and hike the trial out of there to Crystal Lake or do the Duck Pass trail above Lake Mary.
You mentioned the need for a head lamp. On my first summit which was late July, my lights batteries died and it was so dark that I waited until a group of hikers caught up to me so I could follow them down. This was at 8:30 in the evening.
Good luck on your attempt..