I am going to start by saying do LOADS of grid work. It will teach your horse to pick up his feet, and pay attention, and it will give you better balance. It should also teach your horse not to take off so early (although, he is taking off too early) because if you set up a bounce, as soon as he lands he is going to have to be jumping again.
You also need to release MORE. MORE. MORE. :) If you need to, tie a bright orange ribbon in his mane higher up on his neck, and each time you go over the jumps, sttrreettcchhh your arms up to reach that ribbon. Also, instead of relying on the reins, grab a piece of his mane instead.
And as others have mentioned, sink your heels down, and shorten those stirrups. Sinking your heels alone will help your balance allot.