We had a horse with a similar problem. We knew he would accept the bit and he would partially work into the bridle - he'd drop his nose a little and go a bit soft - but never quite there.
We knew this horse was capable and at the correct training level to achieve this.
Daughter had a couple of lessons with a new lady who actually got on him and battled it out with him.
It came down to leg, leg and more leg. ****ed hard work (as doing anything properly is) but is was constant pushing with seat and leg. Not a kicking go faster kind of leg but a pushing leg in conjunction with the 'pushing' seat. (we had this bit).
The instructor, in the end, had to drop her hand low and get quite hard with the rein to make him lower his head - infact she overbent him quite a lot the first couple of times. When she got what she wanted she would release the pressure. Suddenly, the horse realised what he had to do with his head and it all fell into place.
We were able to go back to soft hand - but always and constantly lots of leg.
Wish I had a video to show you but I don't.
A dressage saddle will definitely help you.
Only As Old As You Feel - Sometimes I Feel VERY Old