When I cut hickory backing strips I cut it to 3/16" thick and after dressing up both sides it usually comes out at 1/8" or slightly less. I keep them parallel. Hickory backed ipe makes an excellent bow. Make it narrow or the backing will be thicker than the belly. One onch oe 1 1/4" max.
I have sucessfully used hickory backing on ipe, osage ,locust, mulberry, ERC, black walnut, cherry, red oak and maybe others.