That's a pretty fast jog!!! That's more of a trot than a jog, and it's a pretty fast choppy trot at that. If you can slow him down and get him to stretch out a little, the whole sitting/posting the trot thing is going to get a lot easier on you.
One thing I find helpful in keeping my hands and legs quiet is to think of my elbows as weighted and stretching toward the ground, but not locked up. Then my hands will follow, but they'll still be loose and quiet since I'm not pulling my *hands* down, just letting them follow my elbows. I also find it helpful, when I get on and I'm warming my horse up at the walk, to take my feet out of the stirrups and let them swing from the knees while keeping my thighs steady where they are. Like my feet are weights on the bottom of a string (my shins) that is tied onto the bottom of my thighs. The feet swing freely on the shin, very relaxed. I don't *make* them swing, I don't push and pull them, I just *let* them swing. When everything is good and loose there, then I take the stirrups back and try to keep that loose feeling as I do.
I know it sounds like that would make my legs move more, but it's the opposite that happens. If you are holding tension somewhere, when one part of your body moves, it will make other parts of your body move. If you're nice and loose, you'll be able to move your torso up and down without also causing everything else (like your hands and legs) to move too. If you're stiff, it all moves.