The best way I have found to get 'chargy' horses to slow down and relax is to teach them a 'one rein stop'. All methods of doing this are not the same. We NEVER use a disengagement of the hind quarter at the same time. We just teach them to stop by taking their heads away with one rein. It really works.
I have used this to help reschool OTTBs and chargy arena event horses for probably 40 years (long before it was called a 'one rein stop').
Her is a link to a complete (and lengthy) explanation of exactly how to do it to make it work. I have never seen it fail for this application. How we teach a 'One Rein Stop'
This does not require a trainer and it works way better than anyone would actually think it works.