have you considered a tie down?. Also for the flexing I flex my horse when she goes into her physco moods and I flex her most of the time before I mount up and ride. It loosens them up and then they respect you more to. I keep a firm but soft grip on the rain pulling it to the left and once as she softens and tuches her nose to the shoulder I release. After I while I could barley move the rain over and she would autimatically lower her head and tuch her shoulder. It made her respect me more and loosened her up to. Hope this helps.
No, no, no and NO. A tie down is NOT the solution to a horse who goes with their head up, especially one who has not be taught proper flexion. That will only mask the problem, not fix it.
In order to get her to flex from side to side, first and foremost, put her in a snaffle. Then, take up your rein and pull it to your thigh, kind of up by your pocket and hold it until your horse gives its head to your foot. She will probably try to walk in circles but that's okay, just hold it until she stops and be sure to give at her FIRST ATTEMPT to do what you ask. If she stops and gives her nose even just a centimeter, release her and praise. Slowly, you'll be able to ask for more and more to the point she will be touching your foot. Do this in both directions.
In order to get her to give to the bit, squeeze with your legs, and pull back with equal force on both reins. When she drops her head, or gives her nose, release. Again, reward any ATTEMPT she gives you, then ask for more each time as she begins to understand. You want to be sure you are driving her forward with your legs though, this is VERY important. She may also try to get out of it (ie. Backing, tossing her head, going faster ect) but just hang in there and keep that constant pressure until she tries to give.
As for slowing her down at the lope, put her straight and ask for your lope, when she speeds up, put her on a smaller circle until she slows down then allow her to do straight again. If she speeds up, circle her again, she should eventually learn to slow and go at a consistent speed.
With the cross you have (TWxQH) I'm not sure you're going to get a very good WP horse; however, all horses can be taught how to do the things above.