Sweaty work in draw reins

Today was an absolutely spectacular spring day, and we got to walk around a bit in the sun before our lesson started.  But yesterday Duke had his feet done, and although Brent left his toe 1/8" longer than it was last time, AND put on pads, when we walked down the driveway I thought Duke felt a little sensitive, and when we walked down the road, I thought he felt a little stiff, like he wasn't putting his front legs down quite right, so I didn't walk him on the road, just in the outdoor arena.  We did get to see a killdeer (?) chasing a snake, so that was pretty cool.  A big snake.
When we were warming up inside, Duke felt a little bit stiff - more so to the left, I think - and so I wonder if sometimes when he is stiff and reluctant to bend, it is because his feet hurt.  Which would maybe explain also why his stiffness switches sides.
John had us work in draw reins today, and it was a little warm out (but not really inside) and Duke got very huffy and puffy and very sweaty - even butt sweat.  So it was a really hard workout for him. I even sponged him off afterwards before we drove home.
John had us start out on a circle, get round, go to 10 meters, and then give with the inside or the outside, leg yield towards the outside, and then bend him and give again.  When he softens, the release is to give with that hand, and it's hard for me to feel it fast enough for it to be an immediate reward, and sometimes I can't even tell which hand (or both) I should give with.
So John had us work both directions, then work the full arena, then make circles at other spots along the arena.  Sweet Duke did it all.
Then we cantered, made different size circles, and lengthened.  Here, John had me put my inside leg a little forward and my outside leg a little back, and at one point, he told me to lean back just a bit - to get tall and then to lean back.  He tried having me sit the trot but immediately said to forget it - that the saddle just threw me forward too much for it to be useful.  I had a hard time sitting down into the seat today, but that might be because I put air in the panels last night, and they are super full right now.
After we worked for a while, Duke got much softer - when I'd give with my hands, he'd take the bit and chew it down, and then John would let him go for a while in that longer, lower head frame (or that's how it felt to me).
We had a bit of a struggle on the right lead canter, where John was trying to get Duke to sit down on his haunches.  This was an outside half halt and ... well ... and ... I can feel it, but I can't think of how to say what the aids were.  And Duke wanted to break or move his shoulders out, and it was hard to get him to rock back and sit down, but he did, for a few steps, and I could feel it.
Whenever we did a canter lengthening, I would have to take the reins back up, so when we're lengthening, I'm letting the reins slip out through my fingers.  I have a vague recollection I did the same thing with Charlie.  So it's good I noticed because, like that one jumping lesson with Charlie when the light bulb went off and I could feel it happen - as soon as I can feel it I can start to fix it.
We also had to do some jiggling on the inside rein, in addition to bending, and bending to the outside then back to the inside.
Anyway, it was a great lesson.  Duke worked really, really hard, and he felt really good.  I was impressed with him and with how well we're coming along together.  Of course, we would be useless without John, so my next big goal is to try to lock in more of these feelings and when I feel them so that I can do more of it on my own.
John said that he thinks we'll ride in the draw reins for a while, because it is a good reset for Duke and reminds him what Jane taught him, and he tends to stay good for a few days afterwards.  I'm too chicken to ride him that vigorously alone, with or without draw reins.