Yeah don't bother taking Cottonwood Pass. No water, limited views, sandy. I can't say I enjoyed it much.
I've been over Cottonwood Pass a bunch in the few years and agree with your views. The only reason I use these days is that clears very earlier in the 3-season hiking year. I don't even use NAP. I've come to like Army Pass but I don't take it until August or September because of snow issues.
My favorite place to start a Whitney trip is Onion Valley. This route has more spectacular views than either of the Horseshoe Meadows trail walks. But you have to add an extra day to your trip using this route. We did it in 4 days in '09 but it was a push.