Honestly for a lot of it, the time is almost always made up in the turns. I have a horse that can be pretty quick and runs harder and faster than a lot of my competition, but he has a slow barrel turn. Hence I get 4-5th division times because I don't have the turns down as well as the people running the 1-2 division.
So instead of thinking to make your horse run harder, I would look on how to improve your turn.
Another issue may be that your horse is becoming sour. Another thing I figured out is that my horse stopped running hard when I practiced full speed too much. He also stopped running hard if I slammed him to a stop after running home. I focused on slow and precise runs at home only a few times a month. Then after a run, I always make sure to slow down gradually maybe doing a full circle at a canter, then asking for the walk. I also taught him to rate himself well with a verbal cue, so I didn't have to pull on his mouth at all between barrels.
All of those helped me to avoid punishing him for running hard when I ask. I also would do a gallop out on a soft trails and let him stretch out and run for the fun of it. So that galloping is not always forced and can be fun.
Now its hard to tell how you run without a video. So its hard to give advice on this. But if you barrel turns are good and he is just starting to slow down, carry a crop or over under and give him a wake up. Don't over use it, I only use it if needed. So typically on Jake's lazy day, he gets smacked once coming out of the 2nd barrel. Then once coming out of the 3rd barrel. Then thats it, I always put PRESSURE with my heels (sometimes roll the spur a little for more get up and go) to signal the running. I stopped kicking a little while ago, because he stopped running hard and was becoming sour.
All of my info is trial and error with my boy since I taught myself.