If the handle is only an inch thick or so, if you deflex it before you start thinning the limbs, you'd be surprised how much deflex you can get. Number one, you can get it to bend at all right in the middle, that translates to a lot of tip movement. If you really get a good steam on it.
Number two, you can often induce some reflex or deflex in a green stave, and then set it really well with dry heat.
Lastly, you can often notch a thicker handle, make the bend at the bottom of the notch, and then patch the notch. I have done this by cutting a few, like 3 kerfs with a saw, an inch apart, o the steaming thing and the bend, then drill out where the kerfs were and glue in hardwood dowels sideways.