Sounds like we had the same training (or a like minded trainer at least).
With the exception of headshots or shots past 15 yards I do not get a perfect sight picture, just a flash sight picture. At seven yards the flash sight picture is more than adequate for SD shooting, at 15 yards not as precise but still hits in a 4 inch area or so.
That being said my "flash" sight picture was slow and has gotten way faster. It's really about learning how to go with the recoil of the gun, riding the sights, and having the confidence that as soon as the front sight goes back into the notch that you can pull the trigger and hit around the same spot.
I also use the same drawstroke and presentation. I'm not sure other methods of drawing (sweeping upwards) would be as effective using that technique because you really need to make sure you're leveled off.
When I shoot IDPA I can honestly never remember looking down the sights of the gun except for headshots/shooting around no-shoots. That being said I'm ranked as a high marksman or low sharpshooter in all three semi-auto classes. So I have a lot of room for improvement and could be wrong.