First, welcome out of lurking. It's always nice to see people take the plunge.
As for advice, seeing as you have been lurking, you probably know what my advice will be. Drop the intervals, especially run at that intensity, for a while and build your aerobic base by running more consistently and building up to longer runs.
A couple of things especially stuck out to me.
First, the intensity of those intervals. If you're going to continue doing them, you would probably benefit by backing off a bit. The idea of a workout is to stimulate positive physiological responses. It sounds like you're going out and trashing yourself. This is not the optimal way to stimulate the response you're hoping for.
Second, your theory. It's a pretty popular theory and it makes sense intuitively. Unfortunately, it's not the most optimal way to train. It's better to train both slower and faster than race pace as well as at race pace, with a lot of running slower. The slower running results in much less stress on your body, which allows you to do much more of it and garner much greater training benefit.
You've probably noticed that I've used the word optimal multiple times. There are many paths you could follow that would likely get you to 19:59. The question I see here isn't what is the one way to get you to 19:59. The question is what's the best way to get to 19:59, then if you choose on to 18:59, 17:59, and so on. You might be able to keep pounding yourself into the ground with intervals and get to 19:59. Hopefully, if you choose to do so, you can even avoid injury along the way. Alternatively, you can back off, build an aerobic base before adding less intensive interval workouts back in, and get to 19:59 possibly more quickly and with less risk of injury.