Dressage lesson; Duke "encourages" me to lean forward

Today was pretty warm, and we had a dressage lesson indoors, followed by a nice walk up the low trail and then back on the high trail.  I had a bit of a mental fit about F's news about her horse and his multiple injuries, which was interesting because it's really none of my business, but I got quite worked up about it.
John had us start with 20 meter circles at the trot, with a bit of inside bend, and - throughout the lesson - he had to tell me to shorten my reins several times.  He'd have us go down the long side and then come up the quarter line to leg yield over, then go back on the circle to try to get the feel of the leg yield as the bend around my leg on the circle.  The feeling was, more specifically, the feeling of Duke stepping underneath himself by crossing his hind leg under.
Duke was working quite nicely at the trot, and it felt like fine tuning the bend and making those micro movements that we did the last dressage lesson, where Duke is a speed boat who needs lots of small corrections to stay on the line I want.
We did a couple of the moves from Novice Test B, turning at B and then turning the opposite way at E.  It was helpful to practice it in John's arena, because getting the turn timed properly and at the right angle took me a few tries.
Then we cantered, and it was nowhere near as nice as the trot.  Duke was heavy on my hands, and wanted to see saw his jaw back and forth.  John had to remind me to sit tall, and when I did, I could "push" Duke's butt underneath him, but then I'd start to tilt forward again.  This canter, and the transitions, felt a lot more like when Duke first arrived compared to his canter for the last few weeks. It took me about half of the lesson to realize that's because I had the leftover effect of Duke being at John for the last few weeks, and I've probably finally squashed it all out of him.
John had him moving much better by the end of our work, but it took a lot of effort - doing transitions, going down the long side, and one right lead with a massive counterbend to the left all the way around the 20 meter circle.  We also did haunches in, then bend his neck in, and let his haunches go slightly back out, which resulted in a nice bend around me in three steps.
His instructions were similar to the last few lessons, having me bend Duke to the inside, then half halt on the outside, then sit up, then push him forward.
At the end, I asked about the feeling of tilting forward, and he said that it's the shape of Duke's croup; it's just not the easiest canter to sit down and deep, but I shouldn't be thinking I'm sitting down and pushing him forward, more that I'm sitting upright and tall instead of leaning forward.
It was a good lesson; I was most impressed by how soft and fluid Duke was moving, especially at the trot, and how much the transitions improved from the beginning to the end of the lesson, but I'm not quite at the place where I can totally get that feeling on my own at home.
I said that Duke had been kind of stiff to ride all week and John said that it's part of the show schedule, you spend the week after the show getting them quiet and soft (because he wants to go race around cross country) and then the week before the show getting him ready again.  That's why we work on so many diverse things in the winter; in the summer we're just tapering down, tapering up every other week.