Backing up is also a good exercise to gain their respect for your aids
Nicole, be careful because your technic don't always works, and when it does, it's frustrating the horse. The problem with your solution is that the horse can understand that when he becomes heavy he gets a release and will do that again because he finds comfort.
Practice long and low. If u feel the horse brace on the contact let go off the contact completely. So the horse will learn he can't lean on you.
Groundwork...use cavaletti. Usually the hind end isn't working so the front end is heavy pulling the horse along...they're naturally built like this. Slow the front end engage the hind end and this will in turn teach the horse to use their core. This results in the horse keeping his butt down, front end up, and light in the mouth...your main goal to get carriage and suspension.
PS of Sweden Bridle to start...then tons of balanced transitions. The high jump bridle or jump off bridle may be your best technique. It softens the pressure on the pole and allows for your horse to be more comfortable while riding. Try it PSofSweden.com!!
Very soft rein, don't allow them to have the option the lean on you. Then using your upper body and legs do half halts and down ward transitions. I rode a very heavy shouldered warmblood and this helped immensely to where he was able to go collected on a long rein.