On a practical point, what's the way to reach 'down' with hand/arm signals when using the treat in lowering hand method? Or am I being thick here - umm perhaps don't answer that !!
So, at first, I sat with the dog in front of me, the treat between thumb and forefinger. I held my hand so the rest of my fingers were out straight and my palm was down. Then, I lowered the treat from nose to floor. Both of mine took an inordinately long time to figure out the "down" position doing this (and didn't respond well to the trick of crawling under a leg), but I found when I kept my hand on the floor, they would eventually drop down. After a few repetitions, I'd "fake" the treat, still pretending I'm holding it, having the rest of my hand out straight and making the same motion. Then showing the dog the hand was empty, and feeding from the other hand. Over time, I gradually moved into a standing position - first kneeled, then stood bent over and slowly stood straight, all the time making the same motion with my palm down and hand out flat. I didn't have a problem opening out my finger and thumb so my whole hand was flat. As you start to stand, the hand obviously no longer comes all the way down to the floor; my finished cue is a hand that comes out at about waist height and moves down only a couple of inches.
For our "down", my hand signal went from a treat held between index finger and thumb, pointing downwards, nose-to-floor, to a pointing down index finder (looks similar to the treat pinch), with a slight motion downwards, like I'm pointing at the floor. It just evolved without much thought.
We are like Boogie, hand signal first, then verbal. For DOWN, or whatever your word, the lure with the treat went to the hand being flat, palm down, and arm and hand out straight and moving down. Just about opposite to the signal for SIT which is the palm up and the arm/hand moving up. At first the movement is quite exaggerated but eventually becomes more of a flick of the hand without the whole arm moving too.