I ride a very lazy draft mare. Because she is not mine I cannot change her diet, since that is the main problem concerning her energy but I think I may have something to help.
My trainer taught me a ask, tell, demand, kind of training.
First you ask: maybe a squeeze and a kiss
Then you tell: A kick
Then you demand: Make it happen and back it up with a whip.
The problem is if you keep asking and asking they are going to get irritated but if you demand every time then they are going to become dependent or just angry and irritated.
What I would suggest is ask, tell, demand, and once you find a forward trot, let him walk. Then he will see that if he does what you ask he will be rewarded with not having to work as hard. Its going to take a lot of work but you should really try making lots of transitions. Walk, trot, walk, trot. But every time he gives you a good trot, let him walk.