I have never used draw reins. I am not a big believer in gadgets and quick fixes, I do believe in proper schooling and taking as much time as the horse needs. It is very easy to ruin a horse with them. They may have a place in the hands of a very accomplished rider with very good feel and timing in their hands, but even then they are not used to replace proper schooling.
You will need to go back to basics with your horse. First off you are going to have to forget about where her head is and in what position it is in. You are going to have to work on getting her relaxed and moving her forwards. I would spend a lot of time just riding her on a nice long rein and letting her move forwards, forget about her head, get her to relax and let her move forwards, she should soon start stretching her neck down and forwards maybe even start seeking a light contact. Take as much time as she needs for this to happen, it could be a day, a week a month she will let you now when she is ready. Only then can you begin to start thinking about your contact.
Do you ever take her out in the fields or trails for rides? If you do and you have access to some, it may be a good place to ride her, she will most likely go forwards and more relaxed naturally on her own than in the ring or arena.