As soon as I read the title 'head set' I cringed ;)
If you want to do Dressage with this horse, throw away the concept of a 'headset' and think more about him being a fish, and you are the net. You need to 'scoop' him up from behind to lighten his forehand, rather than trying to pull his head down into a false frame which may look 'pretty' to the uneducated eye, but you will get absolutely canned by any judge worth their salt.
In the bottom photos, he is very much on the forehand and I can see that he is pulling through your reins.
Get rid of the Dr Bristol - they are not Dressage legal - and put him in a french link. It is a similar bit, with the double joined mouth piece, but the 'dogbone' lies flat on the tongue rather than on an angle as the Dr Bristol does, making the french link a less severe bit - and a Dressage legal one at that.
This is a photograph of my horse, warming up at a clinic. Notice the difference in his frame from your horse?
His hind legs are pushing him forward, while his shoulders are starting to lighten and he is not running through my hands, but is lightly accepting a contact, with a soft back.
That is closer to what you want to aim for at this stage. Once he can work in a frame like that, you can start to bring him up, or ride him towards long and low. Once you bring the horse into a 'higher' more advanced frame, working towards collection, the joints will bend more all the way through the hind legs while they take more weight than the front legs. The front legs will then lighten even more, so that you will eventually be able to ride the ultimate in collected canters - the canter pirouette, where any excess weight on the front legs will impede you from being able to perform the movement.
This is the same horse, starting to come a little more into collection, but being worked a little deep as a suppling exercise - he is a horse that naturally wants to be on is front legs, and be very strong in the hand as a result.
This work all comes from the hind legs. Getting the hind legs active, then you can start to get more bend through the horse's ribs, more suppleness through the neck, poll and jaw, swing over the back and then the horse will naturally come onto the bit. There is no pulling backwards or jiggling of the reins required, just consistent regular work, strengthening the hind legs and back until the horse can maintain that position while being soft in the hand and light in the shoulders.
My horse is training elementary/medium level Dressage at present, and I am still working on strengthening those muscles. I do not expect him to hold collection for more than a couple of minutes at a time in training, and in the canter particularly, he is only just starting to soften his jaw and poll to me, while remaining balanced over his hind legs.