First check his hocks. This will account for several of the problems you are talking about.
Next he is a big stepper. This is the type of horse who tends to be a hopper when pushed faster. Meaning he takes a large side step in the turn and is not as quick footed at most turners. Not a bad things but leads to several issues ( not necessarily problems) First is the hopping which you are seeing with speed. Other is the shut down at the end and getting it quick and clean at the correct spot.
As to fixing it. There are several things you can try and some will even help with the dropping the shoulder. One is side pass into the turn. Next is trot and ask for the turn as you are trotting. Then only do one or 2 cross over and trot out of it. Try and get his stride a bit shorter through the turn. Also once he starts his turns take your foot off and control his speed with a kiss rather then your leg. A lot of people will train the turn and bump the horse each stride as he steps out. This causes the horse to take a bigger stop out. Again not a bad things but can (again not always) cause issues.
-I'm so busy... I don't know if I found a rope or lost my horse.
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