When your asking for a half halt or transitioning down, relax into your seat and breathe out. I think a lot of people tense up when asking for transitions, and thoroughbreds really react to that. Also lots of ground work and flat work, if a horse isn’t respecting you and staying behind you on the ground, it will usually be even worse when you’re riding. Hope this helps
Lots of pole work. I found with mine she she focuses more and slows down when there poles.