Backing exercises - including backing up hill. Not in the cart, but before you hook, while on the ground. Back out of the stall and to your grooming area. Back up to your cart. After unhooking, step forward out of the shafts, then turn him around and back him to the washrack or grooming area to unharness him. When putting him away, back him to the pasture or stall. This isn't going to make him "pull from behind" but will strengthen the right muscling to allow him to track up properly under himself to drive with that rear end.
Lounging (and later ground driving) in side reins, sliding side reins or a "chambon". Starting very loose and taking up more to allow them to start accepting pressure and giving to it while working. If encouraging them to engage while working, they will start striding deeper under themselves.
The images on google that I'm finding of "today's" chambons are all run from between the front legs (girth) up to a browband attachment and then to the bit. BUT we used one that only sat over the browband/ear area (no bit hook up) so that there was no pressure on the bit. If the horse raised his head too high, it pulled on his poll and reminded him to drop his head. Then they usually started working longer/lower and that in itself often got them tracking up under them selves. When we were working saddle horses, we often used the chambon on the poll and draped a lead line from one side of the rear of the saddle to the other around their haunches - like breeching. It really made them "think" about their "butts" and you could see the instant change where they'd lengthen their stride from behind. I haven't seen the same connection with breeching on a harness pony, though... I can't explain why!
This is not a one time usage or an overnight training. This is building up to the work and working regularly. It's not meant for babies, either.