Scandias, your question may seem simple, the answer is actually quite complicated. For one, the horse must be “through” in order to stretch properly. Unfortunately many Morgans have strong front ends and hind ends, with the hinge (the back) sort of missing. And without the back working properly, you have no chance of getting her “through”.
If I were you, I would ride her with contact, with loose reins used for reward only during short breaks. If she curls in, shorten your reins so you maintain consistent contact. Don’t worry about her behind vertical. It will happen until she learns to use her back. Start at walk - if she is not through at walk, she ain’t getting it at higher gear. Ask her to be active in her walk. Make sure you are not tight in your body. The moment she pushes her nose out, push your elbows out so she does not bump into the bit. Use a lot of lateral works - leg yields, turn on forehands, spiral in and out, to help her to supple that back.
If she bumps her nose into the air, maintain your hand positions so she put pressure onto herself, and the pressure is released when she brings her nose down.
Another thing to remember is, dropping nose down is not necessarily correct stretch. Many horses drop their noses down along with their shoulders, and just plow on the forehands. In order to stretch forward and down properly, their shoulders must stay up. It could mean they stretch only one inch. Stretch is hard work and test their core strength, so don’t be discouraged if the progress seems slow. Most horses don’t have good stretch until they are solidly into 2nd level.