I really dont think you should be trying to mix up aerobic training, and high level anaerobic training. You are trying to improve maximum speed right? The only way you can do this is by training AT your maximum speed for some period - say over 30 60m, and then letting development and adaption take you from there. But ask yourself this - will you really run at your max speed after a 10 mile run? You may think youre going OK, but you wont. Also, running at 28 - 29 second speed is not developing speed - that is only 14 second 100m pace, and Im sure you have better basic speed than that. The training you are doing is good, and worthwile - but it sounds like a session for improving form, and running economy - especially under fatigue, so i wouldnt stop doing it. But to develop speed, I think you need target a specific day during the week to work on it. Say after a rest day - or easy day. Then you can run 3-4 miles easy in the morning (if you have the chance) and then devote a session entirely to speed in the afternoon. Just do 10 minutes warm-up, some light ballistic stretches (not static) and then some type of speed development - Im sure your coach can help you on specifics, or there will be a coach around willing to help. I would imagine something like 4 x 50m, where the first 20m, you wind up, and then run a flying 30m as fast as you can. Keep it short and simple, and take HUGE recoveries. By devoting a day to improving your speed - you also break up the monotony of distance running, and its fun to have a change - its also like an active rest for you too.
But hey - this is just an opinion - notice i used the term "I think" a lot. Its just what I think, and remember - "many roads lead to Rome" so dont take what I say as law, cause Im not saying I know it all. Its just an idea - take what you like from it, but if you try something like it - I think you could go OK.