A properly designed boo backed bow is not much over that width. The bigger the boo of course the wider the backing strip but usually not much over that.
I personally think hickory is not a good candidate for a boo backing and a hickory bow (IMO)should be wider than 1 1/8" . One thing you can do to improve the combo is to trap the bow towards the belly. This will give you more belly to spread the compression stresses over a wider surface. In trapping the bow you will want the cross section to have a wider belly than the back.