I agree, 1.25" is as wide as you need for whatever you want. You can make a 55lb@28" bow out of a 1" width if you go 66" length for a stiff handle, or 60" for bendy handle. With sinew, you can make a 50" bendy handle bow that is 1" to 1.25" wide.
Native American bows were often quite short, but you have to consider that they were sometimes shorter themselves and/or they drew to an anchor point on the chest rather than the corner of the mouth. And those that used the pinch grip to draw, probably limited themselves to a reasonable draw weight as a result (maybe 50lb which is certainly enough poundage to kill most animals in North America).