I think, instead of trying to go up the hill as fast as possible, you should work on slowly increasing the pace at which you can go up the hill without killing yourself. You will never be riding short hills in isolation, they will always be preceded and followed by a lot more riding. So find a pace where you feel comfortable, go up the hill. If you still have gas left (and you should) then go down the hill and do it again. Repeat until exhaustion.