Considering some of the photos I have recalled seeing of her being ridden; she has learned over time to really, really learn how to evade pressure on the bit by raising her head, hollowing her back, and pulling her nose up and out when any pressure is put on the bit. That means pressure by rider hands, or side reins. Depending on this horse's age, this may take a LONG time to re-modify, and she may still revert back to those tactics if she gets stressed, or has an incompetent rider on her.
I do alot of flexing with my horses to help them understand to "give" to the bit, rather than to evade the bit; I rarely ever use both reins on a horse, actually, since even when I stop, I use my seat to actually stop him. The horses are taught to stop using the ORS, and usually no rein pressure is ever needed beyond closing my fingers around the reins. I usually use nothing more than a simple snaffle of some sort. I have D-Ring, and O-Rings, with various mouthpeices, and do have a sweet iron mouthpeice as well. I don't know that it will help your horse "like" the bit, since how you are using it will be a factor there as well; but most horses like the sweet iron. Most horses like a copper mouthpeice as well.
You have not had her long, nor have you had trainers who have really been willing to help you help her get over this, so she's really been "Stuck" where she's at, simply because of where you are at with her. I think until that changes, you may not see alot of positive change in her. Don't worry so much about her 'head set' either, so much as where her hind end is going; she probably won't have a really low headset, due to how she is built, but she should still be able to drive properly from behind...ie, her hind legs should reach well beneath her when she is working properly, with her back rounded, and hind end engaged.
I have had my mare for 2 years, and I had alot of the same issues with her; we still have some days where she would rather go around the arena with her head raised and back hollow; I just do alot of "cruising" exercises on those days, since pulling on a horse with that ingrained of a habit does no good, and can just leave both of you more frustrated. When I stay out of her way, she starts relaxing alot quicker, and eventually her head starts relaxing more, and she starts driving from behind better, and I can pick up on a rein, ask her to do a circle, and let her go again, do another circle, etc.
Your horse has alot of "muscle training" to do, as well, since her body is likely so used to traveling in the wrong fashion, so traveling lightly on her forehand, and driving with her hindend, is going to be difficult for her. When you do your ground work, do alot of changes of direction, to get her to rollback onto her hindend; this will build up those hindquarters, and help strengthen her muscles back there, so you can start asking for more and more drive from behind.