Radiohead
It seems by your description that cardiovascular capacity is a problem. I‘m not usre how you train but I posted this in a thread in Offtopic: workouts:
"Get into a progressive running program. The CFRC has a good pamphlet called CF EXPRES Jogging. Using the treadmill, build endurance on one day by running moderately, another day running slowly to build endurance, and then another quickly (wind sprints) for cardio and muscular development. You must develop strength, endurance, and cardiovascular capacity to excel."
There may be a host of issues that may affect your cardiovascular capacity, but your heart is pumping to get oxygen around as well as other stuff during training. Make sure you have a diet with decent carbohydrates and proteins. What helps alot of people is breaking up their running routine.
In the CF pre-fitness plan, to run 2.4 kms in 12 mins isn‘t just enough. They recommend being able to run 6 kms consistently.
To get there and improve the cardio, the best way is to mix up the running. One day run moderately, another slowly for distance, the next training day run like kell, slow down for a minute, catch your breath, and run like kell again, slow down catch your breath, and so on for several sets. The fast running gets you close to the maximum heart rate, trains the body to use oxygen better than consistently running slowly, and trains the aerobic and anerobic (sp?) nature of cardio.
By training with fast running sets, sometimes called wind sprints or sprinting sets, mixed with your usual running sessions you can bring your active heart rate down. Another way to do this is to reduce the time it takes to run a mile. If you can run a mile in 10 minutes, try training to do it in 8 mins. I you can do it in 8 mins, try for 6. Over time, your active heart rate should reduce as the body adjusts to the training.
In summary, adding a day in week for sprinting
or training for speed helps.
Its best to go ask an authority on running or look for training tips on the ‘net about training heart rate and cadiovascular capacity (VO2).
Good luck.