In your case I would first get rid of all that loose and cracked mortar. Then reapply a new layer nice and flat and use this layer as base for the new crown. When doing the new crown you will absolutely need some kind of bond break for the new cement, be it sheet metal or tar paper, or the expansion and contraction differential will tear your brick work apart! If you use jomama's design be sure to add a half inch half round down the middle of the two by four to get a good drip ledge.
When I was looking for the new length of flue on my project I found nearly a dozen different corner radii. I laid a piece of cardboard on my existing flue and traced the outline. I cut this out and then had a 'gauge' to carry around to find the correct profile, finally at Hamilton Parker.
Here's a drawing of my project if it may shed any additional light:
I also have a nice article I ran across doing my research about the subject but it's too large, at 476k, to post. I'll be happy to send it to you if you would like. The chimney actually looks very similar to yours.