The only times I have ever used them is on Reeco, Twice. When he tenses and worries his head comes up and I need to get it down fast. Once it is down we are fine but If I don't get it down then he will bolt.
I used draw reins for 2 sessions when I was realy struggling. Yes it takes him over bent but i'm not aiming for correct when that happens, all I want is that head down so that he relaxes, then I drop the draw reins and ride him up into the bridle.
I was taught to use them like you do.