Draw reins, like a German Martingale, are both very useful tools in the hands of a good trainer and are a nothing more than an ineffective gimmick in the hands of a novice.
When used sparingly on tough horses that have been poorly ridden by bad riders, they can really help to get a spoiled horse back to thinking right and not fighting their rider. Used any other way, they just teach a horse to duck behind the bit and dump over on their forehand. Both are worse habits to correct then the original problem of traveling high headed and hollow backed.
I have used gag bits very effectively to get horses working right that have learned to duck behind the bit. Again, they should be used sparingly and gotten off the horse as soon as it learns to come up to the rider's hands.
I would use lateral exercises like 'leg yields' and two-tracks to get the horse back to using its hind end and back. It is difficult for a horse to 'fold up' and yield to a rider's single leg and rein at the same time. Leg yielding exercises and circles with reverse bend will work every time, especially in a gag bit.