I think the first thing I'd do is remove the bark and sapwood then chase the back ring. Be sure to seal the back once you expose new wood. Even on a well seasoned stave if you don't seal the back checks can appear. I use spray shellac to seal bow backs. A couple of coats go down easy and remove easily when the time comes. Then lay out the bow on the back. If the cracks end up in the handle area you may be able to work around them. Generally the handle area remains rigid so the cracks may not affect anything but aesthetics. You can fill them with super glue. Clean up the sides so you can see what you actually have to work with.
Work your way, step by step and at each stopping point readjust your thinking if needed. Post pics as you go so we can see what you have.