A little old, but what I see:
Hands are moving separately at the start. If you can focus on grabbing the shirt faster, while keeping the other hand in synch for grabbing the grip, I've found the faster you move that support hand, the faster your hand reaches the pistol. It needs to be SLIGHTLY slower so that the shirt is clear, but not much...key I've found for this step is: Faster support hand leads to Faster grip.
Support hand pulls up shirt, then takes the time to push it back down. As soon as the shirt is clear, that job is done. Let go, and begin transitioning to the grip, which should already be started pushing out (avoiding the big no-no of letting the support hand get in front).
As other mention, bring everything up to eye level...I like it as early as comfortably possible. I've had situations (fortunately only in competition) where the demand for getting first shots on target had me firing while still pushing out...since everything was already high enough to see the sights, I was still getting good hits. Did lousy in most of the rest of the competition, but did well on that round!