also consider pulling. It can increase your speed going up, which can minimize climbing time, but it also takes more out of you. but it is more efficient, which is part of what standing is about.

while your body is pushing the weight down on one pedal, you are pulling the other up. It eats up the distance much faster.

I'd say this requires much practice, as climbing standing burns me out quickly, but if I calculate how I get burned still sitting, I'd say the energy usage is almost the same. It comes down to my mental ability. If I think I'll collapse before I make it up if I take the "long" way, then I stand, and push-pull up the distance, and arrive at the top panting and breathing, and thinking I did it!!!

You could try practicing standing and pedaling on flats if you are having problems rocking. Your hips should rock slightly, but the bike not so much. Once you get the balance and feel down, it shouldn't be a problem to apply to climbs.