My horse used to be the same way, he was so strong that I could barely control him and would lean so much on my hands and tuck his head down and in, we finally put him in a gag and it's helped a lot, the way it works is when you pull on the reins, the bit is lifted up in their mouth so it picks their head up, I am extremely gentle with it because of how strong it is but it has really helped him a lot
I call it the transition challenge! I use it every warm up. Whether going into jumping or dressage.
Start counting your steps. Pick a number, I usually start with 10. At ten go immediately from walk to trot. Really make the transition crisp and smooth. That's the goal. Count to 10 again and transition down to walk. Repeat this a few times and decrease the steps to say 8 and repeat the exercise. Get as low as you can without losing the quality of the up or down transition.
For the first few times you try this exercise keep it to walk and trot. Once the horse gets the game add trot-canter transitions.
Points of advice: don't pull on the horses head for downward transitions, use your body. It's usually easier if you stick to a 20m circle.
All the best and let me know if you try it.
Seek a dressage trainer in your area, or audit a clinic.
Normaly the horse are heavy on forehand when dont have a good balance... do a lot transitions for promove a natural balance.
You could practice half halts