Are you sure the harness fits nowhere near his neck?
When mine used to wear puppia harnesses they did this too, I realized that the puppia harness actually does go near their throat even though it is a harness and while the weight is more evenly distributed it was actually still putting pressure on their throat area. Since I switched to a step in they are fine.
If its not near his neck, he may just be pulling too hard and putting pressure on his chest.
