I hope that I would be as fast as you. Great speed, and 1.56 at the first year racing 800m isn´t that bad. But you will improve drastically on that.
Shortly what I would suggest to you to improve your endurance of fast twitch muscles, and the slower ones. Since you probably have very little ST´s, you shouldn´t do too much of slow running. But you need it definitely. Short base runs as frequently as you can, with an occasional long run (increase the distance when you improve). These aerobic slow-aerobic threshol runs are really important, although you shouldn´t do too much.
You need to do endurance workouts also at higher intensity. Interval workouts at medium intensity with short ACTIVE (jog) recovery like 200-400`s @ ~your estimated 3k-5k pace/45-90sec jog recovery (or what it takes that you won´t build excessive amounts of lactate), half mile repeats at your estimated 8k-10k pace with ~90sec jog recovery, short lactate threshold-tempo runs/really long (~10min) intervals at that pace. You should be careful on all of these higher intensity endurance workouts, so don´t go too fast. The short active recovery is really important in order to keep the aerobic system going between the intervals, and keeping your heart rate still quite high. You only need 2-3 of these workouts in a week during base training. Remember the importance of short (and longer) easy runs close to your aerobic threshold.
Avoid high lactate workouts in the base phase. BUT the short sprint work should be done with the base training. You don´t want to lose your speed. You probably know how to do the sprint work, but to mention something like from ~50m sprints to longer ones like 150´s done fast but controlled, and both with long passive recovery. Good luck!