Well, first of all, there is improvement. That is evident.
I think the horse needs to be ridden really forward , both at a very forward walk which can be where you work for the quality connection that anebel mentioned, and from time to time just releaseing the reins and asking him to really stretch out and MOVE!
But, to help him do this, you will have to improve your ability to move with him, which means less tension and bracing in your body.
You push too hard down /forward into the stirrup and your leg looks locked, as doe the elbows (which you are aware of) . It is the locked elbows and legs that make it impossible to have a quiet hand. One cannot just "make your hand quieter". you have to make your body softer and more following , in order for your hand to thus be steadier.
So, the slow , walk work is for you to really relax your body,. get your weight onto your seatbones, feel your pelvis following the saddle and moving "through" you hands, which are like a steady gate through which your pelvis moves back and forth. The more you "let" Cinny move you the better it will feel to him.
And the other one, where you just ask him to trot forward, not worrying about direction, connection or anything, just that he stretch out and push forward is to keep him from becoming more and more contracted back behind the bit and leg. to shake off the stress and just let loose a bit.