I had concerns that the wood was still a little wet, so after finding the outline of the bow in the stave, I cut it down to dimension on a borrowed band saw and weighed it to the nearest gram. It lost only one gram of weight overnight, so I placed it in the sun out in the yard for a day or two. I knew it was not soppy wet, more like just very, very close to reaching stability with our climate. At that point, it is safe to push a little harder, so I did.
I left it in the sun for several days, then moved it into my Jeep Cherokee and left it parked in the sun for several days when the temps were in the high 90's. Again, no checks, but it lost 16 grams of weight and then stopped losing. I realize osage CAN get too dry, so I left the stave to sit in my cool, shady garage and checked the weight daily. After a week, it has gained back a just a single gram of weight. At this point, I am very sure that the wood is right where it needs to be and I will start on final shaping, taking out some limb twist and getting the tips lined up through the handle.
Some might think I am taking unnecessary risks by pushing things like this, but I think there is less risk than you are imagining. You simply cannot push that hard on fresh cut wood, of course, but this piece was cut well over a year ago and Stringman knows how to treat it as it cures. However, his relative humidity is a good bit higher than mine. I have given the whole stave several weeks to adjust, following the weight down to the nearest gram. I have checked and rechecked the rate of weight loss all thru the process and I kinda have a feel for when time comes to push and when to back off. I have not had a stave failure, yet. Knocking on my own wooden head!