You have enough speed but you strength is lacking. I think you need to aim for 1:51/1:52 and you are going to need to get your 1500m to a time no slower than 3:50, preferably faster.
Working out more on the track will not get you the rest of the way there. You are going to need to increase your stamina and endurance. That doesn't mean that you abandon the faster work you are doing, it just simply means that you can scale that back a bit and focus the earlier parts of the workout on paces that are significantly slower than 3k race pace, but not all-out.
I think workouts like 5-6 x 1-mile at 5:05-5:15 each will do wonders for your fitness.
Continuous 6 to 8 mile runs at 5:35-5:45 pace will also get you there.
These workouts are going to feel like a walk in the park at first.
Don't forget the long run (easy to moderate) and don't neglect the speed maintenance. Do not let speed be your focus.
Run hills and striders. Run your easy runs slowly.
Run as frequently as you can and do not take days off if avoidable.
A good coach can get you there. Good luck!