Very good suggestions Elana!
I would also have him checked for any health issues as well. There may be muscle soreness, weakness or stiffness which is hindering him from collecting better at faster gaits.
I had chiro/acupuncture done on my gelding and it helped pinpoint exactly where the issues are and helped my trainer know exactly the type of stretches/work that would benefit us. It also helped me understand his limitations and know the WHY behind it. Knowing that makes it easier for me to help fix it and hopefully achieve a sounder horse down the road.