Search:

Looks good to me. Shop for a little slurry stone. Rub it all over till you get some slurry on it. Thin as you go to just water!

Let's see it. Might need nothing at all to do it's job. No more than you use a Thurri, a size like yours will work nicely.
Escher produced hones in your size up to huge ones. Same stone, more...

Not to mention(As you probably already know!), if you are truly intrigued on Coticules, there is TONS of written word on them.
There is even a dedicated forum for them, I believe. My Coti is...

Yes, a great edge is exactly that. I was very satisfied as I bought and learned my 12k Naniwa. A great finisher, IMO.
The gift of the Escher from a friend is truly appreciated. I probably would...

I suppose I would answer with either, OR both, depending upon the razor. Old Sheffield, certainly Escher.
A hard-steel Genco? 12k Nani! A more modern Henckels carbon, 12k to Escher.
...

I am certainly not implying that a Coti is not a finisher. Using many techniques, some can begin, and then arrive at a super-fine edge on them. Certainly this is not the Escher's forte, as it is for...

A Coticule is a honing 'system' to me, while an Escher is a finisher. Seems apples to oranges. I have never been a big Coti fan, unless on really old blades. I think you must be a big honing...