Others are saying basically the same thing. You are aerobically weak with fantastic speed. All training requires "support" from both the speed side of race pace and the endurance side. You have so much room to improve on the endurance side that it hardly matters what you do--everything should produce results. What matters is that your key workouts should be on the endurance side. You should stay in touch with your speed, but make those workouts no harder that "moderate," so that you're fresh for other, endurance-focused workouts.
My advice would be to forget about sustained LT runs. I'd do repeats at a pace slightly faster than VT (basically when your breathing gets labored, and very close to LT). 1 mile or even 1k repeats at VT with a 200/400 float recovery (not a jog, but backing off enough that you start to feel good again). I'd also do some of my "easy" runs at just slower than VT.
You can add some speed work at the end of these workouts to practice recruiting fast twitch fibers while tired.
Progressions are also a good tool. For milers, I like the progression to be shorter and steeper. Whereas a marathoner might start as 6 minute pace and work down to 5:40 over the course of 18 miles, you might do 5 miles with 2 at a jog, 1 at a steady pace, and then spend the last two cutting it down to almost mile pace for the last 400.
Your coach is right that 5k/10k pace isn't meaningful for runners at your level because you don't know what those paces really are and because they don't necessarily correspond to the physiological stimuli that more experienced runners get by targeting those paces.
Very hard to say if it'll happen this year with so little time left. People respond at different rates to aerobic training. The summer and next 9 months are a big opportunity.