I am like Shrapnel and not sure I can describe it, but I will give it a try.
The haul wants to happen in what Lefty Kreh calls the "speedup" or the acceleration phase of the cast, the release is at the stop. The haul wants to be short and quick. Most people tend to pull too much line on the haul but short and quick gets the line speed up and the load on the rod at maximum.
I would suggest not releasing line on the stop until you have learned to time the haul on the speedup stroke of the rod. This is done by retaining grip on the line and following the rod with the haul, basically at the stop your line returns to the grip hand as the release. I know this sounds confusing but I don't know how to explain it. When you have mastered that timing without losing the load on the rod then you can start releasing line at the stop to extend the cast.
As Shrapnel said I use the haul on most every cast to some degree to minimizes the motion of the rod for the same results, so keep the casts short and efficient and then lengthen the amount of line and travel of the rod as skill progresses.
Lefty Kreh has published a good book on the subject and has videos available which I am sure will help you. Since you are experienced with the fly rod the book or video, or an hour of professional instruction, should have you mastering this technique in short order.
