You can get very bogged down over-thinking this stuff. There are all sorts of videos with all sorts of ways to clear covering garments, but I teach the best way is just to focus on the act of getting a full firing grip on the gun. The rest literally takes care of itself.
Let's first look at this generally. You'll find people debating endlessly how to sweep a jacket out of the way when drawing from a strong side holster. Some use the thumb hook approach and defend it vigorously, while others use the cupped hand method and defend it with equal determination.
I simply reach back, get a full firing grip, and bring the gun out of the holster. Think about it: you don't sweep your jacket back when getting your wallet out of your pocket, do you? Of course not. Getting the gun out is no different, yet you can find endless debates about it on the forums, YouTube, and at any gunstore. Again, don't get caught in the trap of endless analysis. Just concentrate on getting a full firing grip on the gun.
If you're carrying under an untucked shirt, the same thing applies: get the shirt out of the way so you can get a proper grip. I usually grab the shirt hem directly under the gun with my strong hand, lift it up enough so that I can get that good grip, and then do so.
The important thing is to keep the muzzle from pointing at your body before it gets oriented to the threat. The drawing in the car video lays out the concept: gun parallel to your body (leg). The same dynamic is at work drawing from a standing position. The CFS book has a chapter on the draw sequence which you may find useful.
For your specific situation: are you using the 5.11 shirt with the "hidden" vertical velcro concealment pocket? In a protective detail, I'd recommend you practice getting through the Velcro with the firing hand, in case the off hand is needed to steer or shield your congregants. Yes, it's faster to rip the Velcro with the off hand while drawing the gun with the strong hand, but faster isn't necessarily more efficient in the context of your probable fight.
Spend time learning your own balance of speed & precision and getting off the vector of attack. If you haven't yet gotten the new version of the CFS book, do it - paying particular attention to pages 118-120, which talk about some concepts that will be very important in your position.
