My 43 year old chimney (in Michigan) has loose bricks and spalling in the top 10 rows for bricks. Looking at it closely, I can see that it never had much of a crown - just mortar spread from the tile liner to the edges of the top brick layer. I just installed a high efficiency furnace (PVC vent through wall) and an aluminum liner for the water heater, so there will not be much condensation, as in the past.
I have 4 estimates with a price range of $1000.
The highest bidder wants to rebuild the top 10 rows then spread some kind of synthetic material over the top that is "better than concrete".
Mid bidder would rebuild 9 rows then cast a cement crown with 2" overhang.
Low bidder would rebuild 9 rows, add a 2 1/2" thick limestone cap that over hangs, then use sloped fiber filled concrete from liner to edges.
Since the old one lasted 43 years and in another 43 years, I'll be dead, how good is good enough?