A lot of us are using the rotational draw method, which is a little different from the method you describe. Using the rotational draw method, you set your shoulders into good alignment with the target before you start the draw. Then you raise your bow and string arms as a unit, while keeping your shoulders down, and point your bow hand at the target. The arrow stays in line with your string forearm, so at this point it is pointing to the left of the target (for a RH shooter). As you draw the bow, the arrow stays in line with your string forearm, so rotates until it is in line with the target as you come to full draw. The bow handle also rotates in your bow hand, although it is hardly noticeable if you have a loose grip on the handle. You commence aiming as you see the arrow rotating into position, so by the time you reach full draw, your aim should be pretty well on target.
In the expansion phase, you rotate your shoulders further into the bow, which feels like you're pushing forward with your bow hand, but really it's the final rotation that's pushing your bow arm forward. This helps to trigger the release, if you don't like using an artificial trigger. I have been using this method for several years, and continue to like it. This method is supposed to be easier on your shoulders than the straight back pull, and helps you to engage your back muscles.
For further information on this method, please refer to Arne Moe's video on YouTube.