I would be heat treating Elm anyway. I’d start by working down to a very rough blank, leaving full width. Maybe take the limbs down to about 3/4” thick. Then clamp to a form and go at it with a heat gun.
I would want to leave an inch or two reflex in it. I would probably not clamp it flat to the form straight away, rather heat and tighten the clamps as I went along.
If you look around for information on how to ADD reflex, you’ll get all the info you need and be able to apply that to take the reflex away