Unless I'm with a group that attacks the bottom of the hill, I don't do that on that long a hill. You're going into the anaerobic power range and then paying for that later. I may pick up the gear and cadence to warm myself up for the hill, IOW bring up the power and HR early, then sit and hold that power and HR as you go down through the gears. As you warm up on the hill, you should be able to increase your speed/power/HR. You want to climb the top half of the hill faster than the bottom half. Just sit it. Don't come up. You're too big for that to be efficient. If you don't have/trust your instrumentation, gradually increase effort until you are breathing deeply as fast as is practical, just shy of panting. Gradually accelerate in the saddle as you near the top. About 100 yards from the top, come up and go hard. You want to reach maximum speed right as you go over the top. Makes a difference in your descent time.
Everyone has a fastest climbing cadence. My long hill cadence (say 3000') is 78. On a 1 mile hill it might be a little lower. You have to play with it to see what's fastest for you. In any case, you'll be fastest in the saddle. On a big climb, I'll get up about every 10 minutes, but you should be up the hill by then. You'll probably do best in the small ring.