You mentioned anything that I would have mentione; being too far leaned forward and that he is coming behind the vertical. I also saw that you are trying so hard to get you legs under you that your foot is turned out and your knee is too tight, stopping your weight from flowing easily down through the whole leg. I am sure over time, as you relax and sit down into the saddle a bit more, these things will almost take care of themselves. It isn't so out of place to stay off his back and ride with a slight forward seat for awhile if he is not used to actually having a rider SIT on him (jockeys don't sit, they stand). He looks a bit stiff in the hind end and the neck, none of which is news to you , I am sure.
I guess I would say relax a bit, sit up more, don't drop your inside shoulder and connect your elbows more to your side.
All in all, you look good and have a very sympathetic seat and hand., This makes me feel glad for that horse being in your loving care. Who could ask for more?