If you're using anything to "pull her head down" you're actually preventing the most important muscle at the base of her neck from working properly to hold the neck up. Artificial aids = bad. The neck and head are just the completion of the horse's hind end engaging and the back becoming round. There is an excellent series of articles in the June, July and August issues of Equus magazine about this very issue. It shows the biomechanical reasons for what different trainging methods to do a horse's neck and ability to collect. Once you read them, you will never dream of using artificial aids again.
You said that she uses her back. If that's so, then she's already engaging her hind end. One creates the other. The next step is to get that energy to flow over her back, up her neck and into the bit. Like water from a hose, you do this by un-blocking whatever is currently blocked. If her head is up, it means there is tension there. It's most likely your position creating it, or else you have her dead straight instead of riding with a slight degree of inside flexion. Make sure you have enough flexion to see her inside nostril and eyelashes. Once you're confident your position is not inhibiting her and you have the proper bend, either transitions or lateral work should get you there.
You just have to see your distance...you don't have to like it.