Sitting trot eureka

After enduring snow flurries and extra-cautious driving on the completely clear roads, we arrived late for a pilates session and lesson with Beth.
The pilates session was great - Beth had to go back a bit because I've been struggling at home with engaging the core muscles - something I can do with her but immediately forget as soon as I leave.  She gave me some simpler exercises to work on at home.
Then our lesson was amazing.  We worked on even weight (I sit heavy on the left - I can feel it under my left thigh), so trying to think about the weight being in the right.  When my left hand crosses over the top of Charlie's neck, that means I'm sitting off to the left and need to shift my weight right.  It's an easy indicator.  I also need to turn my shoulders (but not my head) left most of the time. 
Beth spent some time showing me how when I sit off to the side, it makes Charlie's ribs unable to bend, which is why he's reluctant to bend left but it is so easy for him to bend right.  I told her that I was having trouble with lead changes over fences (from right to left) and also that when we're going left, I put my right hand forward.  She said he actually needs a bit of release to the right.
We worked on 10 meter circles and transitions, and the first thing she had me do was sit the trot and then focus on having the right hip move like the left hip.  The first miracle was that I could feel Charlie's hind legs, so I could time the aids.  Then, I have to think forward and up with the right hip, but as soon as I do, Charlie's back evens out underneath me and he gets more balanced. 
He did all of his lead changes (simple changes, through the trot) perfectly, so he didn't give Beth much to work on there.
But then we took the right hip moving and added keeping my upper body still for the request for the transition.  It was much harder to do on the down transitions, but on the up transitions, if I consciously thought about keeping my upper body still (it tends to lurch forward briefly, just as we do the transition), Charlie lifts up into the new gait instead of lunging down and forward.  Beth said that he mimics what I do, so if I lurch forward, he lurches forward, and if I am crooked to the left, he is crooked to the left.
Following the still upper body and the hip, we suddenly got exactly the right balanced sitting trot, and I just went around and around and around grinning like a fool because it was so EASY to sit.  I didn't have to give him any aids, we just went around smooth and connected.  It was a total delight.  I can't wait to work on that more.
He had a bit of a hard time on canter circles that were smaller than 15 meters, but I think his back was sore because I overjumped him a couple days ago in my attempt to work on three things at once to save time.
I have been feeling down and like a lousy rider, lurching all around and just horrible in general, and I think that is actually a good sign.  I think that it means that we're working on the next layer of the onion, and once this starts to feel good, then we'll have to go back to horrible while we work on the next layer.  But overall, I think this is good - I think this is much better riding than last year, and Charlie is so sweet and generous, just waiting for me to allow him to move freely and then rewarding me by changing as soon as I get it right.