If breathing is a limiting factor, then you might want to try the Douillard, Buteyko, or Oxygen Advantage breathing method. Buteyko and McKeown (Oxygen Advantage) are similar and you can read about them online and watch videos on youtube. I have tried them briefly, but they didn't do much for me, probably because I've been doing the Douillard method for over 15 years.
John Douillard's method is different. It focuses on strengthening the diaphragm by forcefully breathing out through the nose as much as possible.
I learned the Douillard method from his book Body Mind and Sport, published in 2001. You can buy it used on Amazon for a couple of bucks. It has definitely been one of the factors in helping me become a world class age grouper in the 400 and 800.
Like other books, I'd take some of what Douillard says with a grain of salt, but the mechanics of breathing seem to be right. In a nutshell, it's this. Breathe out forcefully by contracting the diaphragm, making a Darth Vader sound, mostly breathing out through the nose. Allow air to flow back in naturally. Don't forcefully breathe in. The air will come in naturally as your diaphragm relaxes. It will take a few weeks to strengthen your diaphragm to handle the new method. It works best at fast paces. Doing it at slow paces will cause you to hyperventilate at first.
The nose can't handle all the volume at faster paces, but even a limited amount of air through the nose creates a lot of physiological effects that would take too long to describe, but the effects will improve your running performance, in my firsthand experience.