Quickstep - the bane of my dances!

With the restructuring of the ISI dance tests 2 years ago, the Quickstep is the one dance remaining for me to pass Dance 8. The whole process of trying to test this dance constitutes an entire story in itself, which I am not about to relate here.
Last week, I started lessons with a new dance coach. Aha, now I once again have a freestyle coach and a dance coach! Somehow, the first lesson wasn't as exciting as I would like it to be. He wanted to know what I wanted to do, and I explained my problem with the Quickstep.

So, these two lessons, we have been working on the Quickstep. Yes, just the Quickstep! He was focusing on how deep the edges should be, where I ought to be heading... how I had to start with the progressives closer to the wall, then the swing for the choctaw heading more into the center... how the free leg on the two forward inside edges have to be extended, etc. It almost seemed like I wasn't doing any step correctly!

Mid-way through our first lesson, he said, "your pushes aren't real!". I was dumbfounded.
"What do you mean - not real?"
"Well, you are not really pushing, just stepping and gliding. You have to push, see there's so much space here. You are not using the rink!"
Oh, I am so embarassed - the rink is small, yet I'm not making full use of the space?!?!

The second lesson, he made another comment that stopped me in my tracks. "Do it slower first. You can go faster later with more powerful push and more knee bend."

Uhh... wait a minute, you first told me to push, yet the push shouldn't make me move fast?? What logic is this?

But I found out that it is possible to push just enough to cover the ice, and yet not go too fast. And it was easier to concentrate on the thousand-and-one other things I have to think of on every step when I'm not trying to think about power from each push. Maybe it does make some sense after all!