The mile is a tough race. However, I think it's one where you can improve, even if your fitness doesn't improve. Getting the pacing right takes practice. Pushing through the second half takes practice. It takes some reps for your brain to find that sweet spot. That's why it's a good idea to race some tune-ups as a lead-in to an important race.
Keep working at it, and you will definitely improve just by improving your pacing and feel. Set a goal of getting the feel of those first 2 laps locked in.
Another part to work on is that stretch from 1000-1400m when it gets physically and mentally hard. Everyone can flip that switch with 200 to go because you know it's time to empty the tank. One workout you could try is ... miles at a steady, challenging pace with 1000-1400 at slightly faster than race pace. For you maybe 6:00-6:10 miles with the fast section at 74-75 seconds.