My tb has ks too, but fused. ROUND BACK. Rooooound back. Not a second with a hollow back, long and low, push him with your seat and leg. Forward forward into the contact to create roundness. Don't do my bad habit and pull them into your hands.
Lots of walk to trot transitions. Working trot to slowing down the trot for 4 strides then picking him back up again to a nice impulsive working trot for about 8 strides. Just repeat this and see if you get any results ☺️
Hill work. Pessoa work. Pole work. If you have access try a treadmill. Lots of in hand work! Good luck! :)