Flints;
I have an idea on how to help you with the "snap" part of your shooting... There is a Mediaeval re-enactment/re-creation group called the Society for Creative Anachronisms, Inc. (you may have heard of it - or not). The archers in the group(s) hold many competitions, all over the U.S (and in Europe and other parts of the world), and one thing they do is called a "Cadence Shoot". Count out each portion of your draw/release: Take an arrow from the quiver; nock the arrow on the string; draw the string to anchor; AIM; release. Do everything to a set rhythm, and it will start to come together. After a while, you will be able to control how long each portion actually takes, and you will -- hopefully -- no longer be hurrying your shots.
And a way to shoot fast -- without actually hurrying -- is to practice loosing (shooting - but why would you want to shoot your arrows? That would just break them. You shoot deer, bears, elk - you don't shoot arrows..) as many arrows as you can (ACCURATELY, of course) in 30 seconds. I've seen a few who can loose up to 9 arrows in those 30 seconds, with excellent accuracy; I usually get only 5 off the string and into an 8" group.