There is one dressage technique that might work for you and the horse. It involves what I call riding the horse in your finger tips, with a light but constant contact. It requires that the rider ride 90% of the time with the fingers slightly open, and just enough tension in the fingers to have a secure grip on the reins, so that while there is contact, it is very light. If the horse is moving faster than the rider wants, the rider closes the fingers of both hands without moving the hands backwards, or changing the elbow position. When the horse ignores this subtle change of rein tension (which he will do until he figures it out), the rider “shuts the horse down” by abruptly tensing every muscle from finger tips, through all the arm muscles, and right through the shoulder muscles and including every back muscle, BUT WITH NO CHANGE OF HAND OR ELBOW POSITION. This must be done solely by changing the tension in the muscles from finger tips all the way up & through the arms, shoulders & back. I also call this sudden tension of all these muscles “running the horse into a non-existent brick wall, because if done correctly, that is what it feels like to a horse who is used to being ridden with a very soft contact. Shutting a horse down like this is a disciplinary technique, a SCREECH of “hey, I asked you for something, & you ignored me.” The rider needs to hold all these muscles locked until the horse comes to complete (and frequently irate and head shaking) halt. Once he comes to a full stop, hold the lock for a slow count of 10 to point out who is really in charge, then release all the tension, again without moving the hand or elbow position. This only works if the rider is able to ride 90% of the time with a very soft contact, with no or almost no tension from fingertips right through the back, so the first thing the rider has to do is learn to control these muscles, so that the rider has the ability to choose how many sets of muscles to lock. Once the horse is used to being ridden with slightly open fingers & a very soft contact, and has gotten over his/her initial shock of being shut down merely by tensing muscles, the rider can start to learn to control these muscles in groups: first group = fingers, 2nd group = arms, 3rd group = shoulders, 4th group = back muscles, and the rider can learn to apply apply tese muscles in groups (first fingers, no response? add arms, still no response, add shoulder muscles, still no response, add back muscles) until the horse either stops or slows down to the desired speed. Although if it takes the back muscles to get the horse listening, the rider probably needs to do a complete shut down, and hold for a slow count of 10, because the horse really wasn’t listening. Once the rider and horse have mastered this technique, the rider has incredible speed control just by tensing or releasing groups of muscles. It really does feel like the rider is holding the horse in his/her fingertips. Better yet, the horse learns to work with a soft mouth with very light but constant contact, and is rewarded for listening to very subtle changes in the tension of the reins. Since you only tend to have this problem in the show ring, you will like that the judge never sees the speed control happening because the hand & elbow position never change.
This is not an overnight fix, it does take time to teach the horse to listen to these very subtle instructions, but it can give the rider incredible speed control, both to slow the horse down (by closing the fingers) and get more energy from the horse either with more speed or more “oomph” from the rear end resulting in a longer stride (by opening the fingers).