Osage is about the most forgiving wood, but why bother spending money on such expensive staves when you can find about any other wood much easier and cheaper.
The advantage of board bows is that they save you a lot of cutting and chopping wood from logs into staves and so on. All you need is a table saw, circle saw or band saw, a rasp and a scraper and you can make a shootable bow in an afternoon. So what if the first five or so break, as long as you learn from them you'll make progress. Chasing a ring on an osage (or black locust) stave will teach you much less and take as much time as building five bows, while being boring as hell.
Say you make 5 cm (2") wide inner limbs of 14 mm thick (a bit less than 5/8"), the handle only needs to be 19 mm thick (3/4") to just have a bendy handle 1" wide. There's plenty of boards you can use for those bows. On a 66" pyramid board stave this will give you the required draw weight, if not more.
Gluing a handle to a flat board surface isn't a big deal either. If you find a board that is already the right thickness (some 12-14 mm thick, 1/2"), cut it into a pyramid shape and just glue a handle to it, and it might not even require tillering, like this one here:
http://www.primitivearcher.com/smf/index.php/topic,56290.msg769585.html#msg769585From the pics you posted, it seemed the outer and mid limbs on the long string weren't bending enough, and the inner limbs a bit too much. That may have contributed to the break. Also, it seemed the limbs were still rather thick (how thick were they?), putting a lot of strain on the back.
So while you're looking for decent white wood staves, try some more straight grained boards and learn from them.
Joachim