Nice job, low set, lovely tiller.
I hope you will be lucky with the thin rings in the long term. My personal experience in one of my early bows of osage that had thin rings, like pages in a paperback novel, was that a couple popped during shooting. I heard the sound and checked the bow, easily fixed with a rawhide patch on the back. Its tiller was pretty average, and the "pop" happened at a tool mark that hadn't been sanded off properly.
A fellow shooter at an archery tournament had the same thing happen to him, his bow was about 2 years old, nicely tillered and was thin ringed.
Another guy I know had a thin ringed stave, with especially spongy early wood barely got pass brace height before it broke.
Despite having thin rings many osage bows don't develop problems, thin earlywood, wider design limbs tend to fare best.
My preference with thin ringed staves is to back with rawhide from the get go just for precaution.
So if the unfortunate does happen, stop shootin,g back with rawhide either the effected spot, or better yet the whole back.
Hamish