The first time I climbed Whitney, probably back in the late 1970s, I had horrible altitude sickness and could hardly complete the climb (even after acclimating by going in over New Army Pass). The second time, last year, I had absolutely no trouble at all at any time during the trip. My secret was similar to bob's, but a little longer. First night in Yosemite Valley (4000'), then a night just above Little Yosemite Valley (about 8000'), another near the same altitude, a third in Tuolumne Meadows, a fourth near Garnet Lake.... a few more high passes, around 200 miles of trail, 22 total days, and then presto! We were on top of Whitney with no ill effects whatever! Definitely the recommended route.
I said "Come to the mountains and get their glad tidings," and they came, oh boy, they came all right!