I doubt you stave is at 10% MC after 3-4 weeks unless you are keeping it in a drying box. Regardless, chase a ring(seal the back again), rough it out, then weigh it. Wait a week and weigh it again, keep doing so until it stops losing weight for a week or 2. Then you can be pretty sure that you are in good shape to continue to till the bow, a thick handle area will still be high in moisture but the working limbs will be fine. My best guess would be if you rough it out today you would be at least 6 weeks out from tillering, unless you use a drying box. Good luck on the build.
Mike