The thickness of the backing has very little influence in the ability of a backing to overpower the belly. It has more to do with the choice in materials (woods). After all, the surface of the wood is doing most of the work, not the area 1/8" or 3/16" inwards.
You need to trap the back to make the most use of a hickory (or bamboo, for that matter) backing for red oak. Make the back about 3/5 or 4/5 of the width of the belly. And keep the belly flat, while the back can also be crowned a little instead.