Also to the OP...
Confidence is everything.
This will quickly break down into the same old "quality vs. quantity" debate you frequently hear on this board. Both sides will present endless arguments: none of those matter to you right now. It's July, and the season is approaching.
You picked the mileage route as your way to the top this summer, so stick with it. Forget the people who are telling you no; they aren't you or your coach, and know little about you. Again, stay with the plan you have chosen.
More importantly, you've decided to not let talent decide the outcome of your races, and have chosen to work more in the hope of running faster. Whether it was the "run faster" option or the "run longer" option for training, GOOD FOR YOU. You've accepted the challenge, and want to become a better athlete. Outstanding.
For now, forget the kids who are "quality" or "low mileage" training success stories; you've not chosen that route this summer, so they are irrelevant to you in your current situation. Instead, let's give you some examples of recent athletes who DID chose your route - mileage - to the top, with the hope that you might draw some confidence and inspiration from them.
From the Olympic trials...
Galen Rupp - 2nd at 10,000 M, 70 miles a week in HS including a 16 mile long run.
Matt Tegenkamp - 2nd in the 5k, up slightly over 60 in HS. His coach also produced 3:49 miler Joe Falcon.
Chris Solinsky - 4th at 5k, up in the low 70s in hs for Steven's Point. His High school also produced sub 4 1500 girl Suzy favor Hamilton.
Throw in the Marathoners (Ryan Hall and Dathan Ritzenheim both were up over 80 MPW in high school), and you have some good people to look at for inspiration.
Good luck this fall. May your efforts pay off in the type of races you are hoping for.