Gallop with some fences

Yesterday's lesson included lots and lots of laps of galloping in the big sand arena, then a couple fences, then some more gallop.  Then a two minute break, then do again.
My conditioning (and running) has not made me a superwoman for galloping at the two point.  Charlie and I were both breathing heavy, streaming sweat, and getting slower and slower (my form got lousier and lousier) as the lesson went on.
All the fences but one were pretty decent.  We did the same lines as last week in our group lesson, but coming off of a gallop until several strides away.  This made me more confident about how to ride them, but I still missed one left hand turn.  Good news is I felt it coming strides away and just didn't react in time - I missed the center of the first fence and it totally threw off the line to the second fence.  A great mistake to feel in a lesson because I can totally see how I will need to be very precise and careful at the show.
One interesting thing was how much farther out John told me to sit up than I would have, and to balance him.
Another was that when I gallop, I kind of throw the reins away.  John had me keep contact and keep him round.  So maybe my gallops haven't been as much of a waste, because I haven't been doing them right anyway.
John also told me to make a single bridge, which is a bridge but just in one hand, and one hand just has a single rein.  That way you don't have to let go of both to use the free hand.  He said he usually holds the double in his outside hand.
He had two comments about my form - flat back not rounded back and heels forward and down.
We had to start turning in the air over the first fence to make the second fence in four strides, but this wasn't as hard as I thought, if I thought about it in time.
Charlie absolutely refused to get the correct lead or change leads.  If I landed going right, he'd land on the left lead, out of spite as best as I could tell.  If I tried to do a flying change, he'd just toss his head up.  If I put him on a circle, he'd just counter canter.  If I broke to a trot, he'd pick up the incorrect lead again.  John was laughing but I was steaming.  Ashley told me before the lessons she untaught Nick his flying changes because they have to counter canter in the dressage test, and he would offer the change. She says she either lands on the correct lead (most of the time) or does a simple change.  That was good to know, except my simple changes at Aspen took too long and we always (except for this lesson) land on the right lead.