Thanks for the input gents!

First, I will collect the material necessary to lap the coticule as described by Josh Earl... once that job is done, I will give the honing another try... actually, my coticule looks like it is flat, but that might not be the case.

@Bart: I will keep you posted on the progression and maybe I do need another cotigura... my rubbing stone is quite large (about 1.5cm by 5cm), is it possible I do not put enough pressure on it to generate thicker slurry? Anyway, I will put a picture of the coticule online as soon as I have the time to take some pictures

@Howard: I bought my coticule here in a shop in Belgium and I have no idea what quality grading it got.

Best regards!