Gotta to say guys....With what I have seen recommended as "go for it" at times, makes birdseye maple look easy, at least belly wood. Is it ideal? hell no, but by no means is it the worst wood i have seen get the go ahead on these boards. It's about challenge isn't it? I cut figure woods for years, curly, quilted, burled are a no go. Birdseye depends on how much, and keeping the figure from the edges. My opinion.
You could back your bow with hickory, oak, maple whatever....then thin the birdseye (Almost veneer like, and glue to the back) the effect without the risk.
VMB