Hmmmm... I've never climbed while in the drops.
I tend to sit up a bit straighter and ride the flats of the bars on extended climbs. I seem to get incrementally more lung capacity that way as my lungs aren't all scrunched up, and that in turn gives my muscles more oxygen and they seem to last longer. Also, I try to breathe a little slower, and as deeply as I can with as full an exhale as I can manage. Seems to help me last longer. On short climbs, I just hammer them as fast as I can, while (ideally) keeping to a smooth predetermined cadence. Sometimes I stand and climb short runs without shifting down as well, as long as I can keep my desired cadence up. But always on the bar flats - never in the drops.
Conversely, I like to hit the drops on long flats when I'm spinning along, and also on descents.
See:
Hills/Climbing Tips