Chimney coping

[Mattg4321]

Another chimney related question. 
 

At the moment my chimney has a brick ‘corbel’ overhang 1 course deep, with flaunching directly on top. 
 

It’s in very poor condition and some of the bricks in this course have spalled. I’m going to remove the whole top of the stack.
 

Ideally, I’d like whatever I use to have a drip detail on the underside - obviously not possible with brick, unless you try and carefully use a grinder? What about normal wall copings such as the below? Will the flaunching bond well with the smooth finish of the coping stone though?

 

Ive also seen rosemary roof tiles used, but again, no drip profile. 
 

Am I overthinking this?

[Mattg4321]

https://www.wickes.co.uk/Marshalls-Smooth-Cast-Grey-Coping-Stone---140-x-600-x-50mm/p/154406

[dpmiller]

are concrete chimney tops not a thing where you are?

 

https://www.carryduffbuildingsupplies.com/small-chimney-coping-27-x-60-686mmx1524mm.html

[Mattg4321]

There’s a few around on period properties, but no idea where I can get one from. Google isn’t helping, which is why I thought of a wall coping. 
 

Either that or replace the corbel course with blue engineering bricks

[Oz07]

I'd of thought any stone cill supplier would knock you one up. Obviously it would cost as bespoke. I've used Serene Stone before, try them.