Bula, I don't think the rest intervals are the primary issue that needs attention here.
I think your work intervals are too short. Your coach is right, your training should be specialized, but what he didn't tell you was that it should be specialized at certain times.
This is an aerobic sport. And your general training should aim to build your aerobic engine as much as possible. Case in point, track sprinters do road rides.
10-minute intervals are too short for general aerobic development. Try the 20-minute intervals at L4, or even longer. (2X20? I'm doing 4X20 these days. Those are tough.) Also, try 2-3 hours at tempo. These are the meat and potato workouts for a lot of the people on here.
If I read it right, your VO2 intervals are 3 minutes. And again, that's not long enough. It's been addressed on this board before...you should shoot for 5 minute intervals at VO2 max. Try 5 or 6 in a workout. And if you can't hold the power, back off to a point where you can and complete the duration of the interval. Also, be conservative with the number of VO2 workouts that you do throughout the year.
As you said, your workout is tougher than 2X20s, and Andy touched on this, but that doesn't necessarily mean that it's going to lead to sustainable improvement. What I've found is that if you back off on the intensity just a little bit, but hold the efforts for longer, you'll see your power keep on going up. And when you want to tune up for the specific events you are going to be doing, then you do some workouts that are tailored to the events.