I had to do a similar thing to put a handle on my Dawn blacksmiths post drill.
However I split the timber first, then glued it back together with a piece of paper in the joint (I'd read about that somewhere). I then turned up the handle on my lathe. The two halves were easy to split along the paper joint. The advantage of that method is that you only loose the thickness of the paper, not the width of your saw kerf, when gluing the handle around the shaft.
Attachment 463518 Attachment 463519
I think your finish is better than what I achieved. I now have a better lathe (but probably not better turning skills :C).
Nice work. It looks good.
Cheers, Vann.