Hi Julian, If you can get hold of a gooseneck scraper(carbatec once again), they are very good for cleaning up growth rings, after the sapwood has been removed.
That is pretty thin ring structure, bows can be made from stuff like that, but it would be worth backing with rawhide, because they can pop a ring down the track. Best time for that is when you have got it to full brace height with a good tiller. You can get rawhide strips from leather sellers like Tandy, Birdsalls etc. Goat, calfskin, or even kangaroo.
Do a bit of practice on a ring higher than one you want to use, as it can be easy to work through thin rings. When you have a small continuous section done and you are confident with what you are doing then try for the final ring.
Hamish.