You have to be careful with her back, if it's too long she might get back problems more easily.
I'm not around racing horses a lot, I guess if she sees other horses trotting away she tries to catch up to them and pass them?
My suggestion would be that you go on a trail ride with a friend and she trots away from you and you try to keep your horse in a walk, if she tries to run after. Walk in small circles so she can't go faster and if she is doing fine trot after your friend. Take it easy at first and after a couple of weeks your friend canters away from you and you can keep her in a walk, I guess that will help you a lot in endurance.