I would lengthen the blackstrap a bit, (and take up the crupper to keep the same length total) to move the hangers back, then raise the rear hanger.
The breast collar should hang in front of the withers instead of on the withers, and you may have to raise it up.
What kind of cart do you use? On straight wooden shaft carts, I always have to move the footman loops forward so that the holdbacks pull the breeching forward. On my marathon, I hook the holdbacks in the shaft loops, instead of the footman loops, and the breeching is MUCH more stable.
ETA: move the saddle back a little, so that it sits behind his withers. This may solve the blackstrap problem. If you are planning to show, be advised that driving judges are not crazy about the draft style harness which has no tree in it....
I don't break horses, I FIX them!