I'd back the entire bow with rawhide if it was me, looking at your picture. On some staves you'll find that you can't just scrape a ring flat, you need to use a goose neck scraper, it has multiple round edges to use. That way you get into the valleys better. To me it looks like there's a lot of early wood left on the back, and in some places some latewood. The bow might hold up just fine like that. I remember the first osage selfbow I saw, it had a ton of violations, it was real dark like it had been around a few years, but if it were me I'd feel a whole lot better with a solid back, one with a good ring or backing. A patch will always look like a patch.