I'd narrow to the current narrowest width, the 1-1/4" you mentioned, and make a bendy handle. Then keep all the width you have until at LEAST 1/2 way out the limb, maybe only taper the last 1/3rd. Even with the narrow profile, your limb won't be very thick.
A Cherokee bow would work, but a modified Cherokee that narrows at the ends, or skinny flatbow makes the most sense.