Half halts and the importance of a proper jumping warm up

While we had a serious improvement in our jumping, it was a rough lesson.  John had us do lots of flat warm up - bending Duke outside, then inside, then changing direction, making 15 meter and 10 meter circles, getting him very round, asking him to go forward a bit, and then asking for half steps.
He then started us into the fences right away, and told me to keep the canter the same as it was on the flat.  Duke did great until we started the combinations, and then he'd rush a bit on the far side, but he'd come back pretty much right away, as soon as I gave him the aids.
John had me at the end work on circles again, more trot, and down transitions, similar to the warm up, but a bit more focus on bend.
Duke got pretty sweaty, and I was struggling, but I'm not sure why.
We started with a cross rail, then vertical, then changed directions over the black and white vertical, jumped the plank, then the plank to oxer, oxer to vertical, then slightly bending line oxer to vertical.
A few times we had to circle 10 meters or 15 meters in between, but Duke quieted down.
John said that I need to commit to riding modified and then prelim; that Duke can handle the height and the dressage test (if I ride it and don't wuss out), and that it's just modified.
He said that when I'm riding, I need to ask for more from Duke.  Ask him to be round and don't let him get away with flipping his head and blowing me off.
I'm glad we did better, and I'm glad he worked me through the warm up I need to ride, but I've been pretty anxious about how far we slipped (and today I felt super out of shape and fat, even before I got to the lesson - not enough hours so I'm half-assing everything) with show season starting next weekend.  I'm not sure we're ready for the big leagues, even with the step in between.