I would sleep at Whitney Portal first night or Horseshoe Meadows, rather than down in Lone Pine. Sleeping at altitude (moderate altitudes like the Sierra) is best for acclimatization.
I've climbed Rainier and Whitney a couple dozen times and have found that for a 2 day ascent sleeping at altitude the night before is more of a hinderance than a help. I find I am better off getting a good night's sleep down low. My mantra is usually "climb high, sleep low". And in fact your body is not going to be producing any new red blood cells in one night anyway. True acclimatization takes weeks, not hours. In fact up until you pass about a week at altitude you usually feel better at the beginning then progressively worse each night. In the lower 48, my strategy is to get up and down before my body can get too fatigued. I agree that ibuprofen and caffeine are the best tools - diamox is way too much of a hassle - you'll be peeing at least 4 times in the night. Also, avoid alcohol and don't be out of shape.
I am taking a few friends to do the Mtnrs route this weekend - it's going to be a cold one!
