I own this horse.
An extremely helpful exercise was Vera’s Magic Circles (I clinic with Vera Kessels). Do a 20m circle between B and E. When you cross center line, circle out 10m. When you hit B or E, circle in 10m. Just keep going on the circles and don’t get in any arguments - let the circles fix it.
Start in the trot (walk doesn’t have enough energy at first) and then add in canter after your 10m circles out (ie between the circle out and the wall). Do your down transition right before the circle out and do the 10m trot circle out immediately after your canters.
Live on these circles.
When they are better, start adding a renvers feeling to everything. Haunches out of the circle and outside bend. Eventually when she braces you can respond by asking for a step or two of renvers and fix it that way.
Only when you are here and the renvers moments are easy should you start trying halts. Walk around with a soft, long neck and try going in and out of the halt without any bracing. Start with only two or three per ride. But it’s fine to put the halts away for a while until your other work is flowing softly.
This process can take several weeks to really get right, but you should see little improvements each ride.
I don’t believe in using a heavier bit, or backing her up after each halt. That in my opinion is a recipe for a rearer, and it’s too confrontational and aggressive imo to put the horse in a learning mentality. She should be comfortable trying to understand you, not trying to protect herself from you, and I believe that a lot of heavy mouthedness is mentally the horse defending itself/protecting itself from the rider rather than reaching out to the rider and letting them in. If you ride aggressively you perpetuate the mental root cause.
Fix the contact going forward and flowing first and then do halts when you can have the conversation quietly without getting loud with your aids. The other way to think about it is that you fix the contact side to side (one rein at a time) first before you fix it front to back (both reins at a time).
When I say I had this horse I promise you I had this horse. These exercises really and truly work. Now he is light and soft and understands so much better. No more wrestling match!