Never say never, I like to say. BUT, you are asking a whole lot out of 44" ntn piece of wood. Especially with a non-working handle.
It doesn't take long to get used to short drawing a bow. I'd say, make a bow with it. With your stiff handle AND sinew, you can probably get 22". With a working handle, you might get 24-25". Your tiller will have to be near perfect. Even with sinew though, it will probably take some set.