I do like draw reins, but on the right horses. He's definitely not a suitable candidate for them by the looks of him, and also you seem to be inferrring that you ride reguarly in them. If I use them on a horse, it is one that goes with it's head sky high and clamps it's jaw. Two or three rides in draw reins and they get the idea that it's far more comfortable to drop their head to a more controllable level, then you can take them away. If you are experienced with the use of draw reins and understand exactly what their purpose is and how to use them without encouraging the horse to come behind the vertical and build incorrect muscles then they can be extremely usefull. But as I said, only on certain horses and if you know hwo to use them properly. They're not a gadget that can be used lightly just to get a horse's head in.
I hounestly don't think you need any gadgets to drop his head, he certainly doesn't carry it at an extreme hight. Your issue is more a full body, engagement issue than head carriage- most head/neck issues are ;)
First thing I'm going to point out, is you said he tries to pull the reins out of your hands and you give them to him. In doing this you have trained him to pull the reins out which is giving him a release of pressure. He is going to use this to avoid work and you will eventually create a problem that is going to be alot harder to resolve.
When he pulls on the bit, kick him and keep your reins. He will get a shock initially that you didn't give the reins, and most likely he will put up a bit of a fight. Doesn't matter. Who is training who? If he fights, keep your reins exactly where they are (hold into the saddle cloth if you are not so good at balancing on your seat keeping your hands steady) and leave your leg on until he gives and settles back into a rythem. THEN you can give the rein a little by straightening your arms slightly for a few strides, then take the contact back. He needs to learn to accept a contact and understand that it is more comfortable to relax in the bit than to reef them out of your hands.
In some of the photo's you have posted, yes he has his head 'in' and 'pretty' and if you go into a low level dressage competition which has judges that don't know what they're talking baout, you may score very well because he keeps his head tucked in. But this is NOT what you want to have. I'll bet if we saw a video of him moving he would be all legs and no back with a set neck.
To combat this, use the above technique to get him giving to the bit (so don't give them away when he wants to grab them) and get him going forward. So think of kicking him on so that he is stepping further out, but don't allow the trot tempo to be any faster. Use your back to keep the rythem that you want to be trotting at and don't let him take you at his speed, it MUST be your speed. Just keep rising at the pace that YOU want to be at, maybe listening to a song that matches his natural rythem will help you focus on counting the 'up downs' and keeping them even.
Put your leg on and expect an immediate reaction, if his hind leg does not react by pushing hard off the ground and coming under him, then give him a good kick, no reaction give him a flick onthe backside with a dressage whip. He MUST react in the hind legs to you leg aids. My horses now know that when I put my leg on and close my outside rein, their inside hind HAS to work harder and they MUST soften the poll and jaw.
Once you're getting a good reaction from the hind leg to a single leg aid, then start introducing literally MILLIONS of transitions. Particuarly those between trot-canter-trot. Canter-trot -canter transitions are the best transitions you can do to work and relax a horse's back muscles. I usually warm up after a nice long free walk, with canter-trot-canter transitions on both reins until the horse has started to give his back and carry me. Then I'll go back to walk for a while, do some trot leg yields then start my session.