headdesk...sorry but if I read one more post about flexing a head or pulling it down with reins to get a horse to relax, I am going to lose it.
OP, see how you are traveling in a straight line? There is the primary flaw in your training. To get a horse to relax and to stretch, bend has to be present. Not the neck, the body. Forget about everything on your horse that is in front of the withers. You need to learn how to manipulate the shoulders, the hinds legs and get that thing you're sitting on, it's mid-section, to bend.
Think inside and outside. Stay on large circles and stay off the railing. On every circle, you should supply the horse with a nice supple inside leg at the girth for it to bend around and a supporting outside leg just behind the girth to keep its hind end from swinging out. You control the shoulders with your arms, which are an extension of your reins. Outside rein gives the horse support to step into, inside rein acts as more a gentle massaging rein to keep the bend.
If you take lessons or are good at self teaching, learn leg yielding, turn on haunches and turn on forehand. Those 3 things alone at work wonders at the walk for unlocking all the stiff parts. Once you have your horse loosened up at the walk, stay on those circles and trot only a few strides at a time. Every time your horse starts to stiffen up, come back to walk, re-establish softness and go back to trot.
I cannot stress this enough. Forget about the head and neck. Absolutely nothing happens there that affects bend. Do be sure to follow your horse's motion at the walk and canter with your hands or the back will lock up and not be able to relax no matter what you do. Also be very careful to provide nice quiet hands at the trot. The less noise through the reins, the better. Hope this helps. Good luck.
You just have to see your distance...you don't have to like it.