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Keith, I'm certified to teach the two courses you've completed. (and 3 others as well) We teach a two-handed slide release - The exact same method, both, Lou Chiodo and Massad Ayoob recommend. It is not a, 'slingshot technique'; instead, students are taught to place the support hand, palm down, across the top of the slide's rear end, close the grip, and pull the slide all the way to the rear. At the point of rearmost travel, you should open your clenched palm and let the slide move forward under it's own force and weight. (Do NOT ride the slide forward with your support hand!)
Yes, it is a matter of using your gross motor skills - the only kinetic skills the vast majority of people have available when they are severely stressed. It is, also, a matter of firm purchase on the slide. A gamesman will find advantages in using one form or another of the slingshot or slide stop/release methods; however, when stressed, 'You will fight as you have trained.'
In this regard I only train one way, and only play at gun games occasionally. (IDPA once a week) I shot with two fellows this afternoon whom I usually don't shoot with. Both of them commented on my two-handed speed. One guy hit the nail right on the head: He said, 'You've obviously been practicing!'
Well, yeah, that's it. If you have to stop to think, you're going to slow down. I often don't use the gun's sights for exactly the same reason. It takes me too long for my eye to find the sights; it's much faster to just, 'shoot off the back of the slide'. I've done so much of this that I can no longer tolerate the drudgery of postal target shooting. If I slow down and concentrate I can put one bullet on top of another; but, I'd much rather double and triple tap an entire magazine into 3 or 4 nine inch plates at 15 yards. This is how I usually shoot a Glock pistol; and, if you want to better prepare yourself for pistol CQB, I'd suggest that you set up a similar training routine for yourself.