I've been using myArmoury as a research tool for many years. It's a fantastic resource and the information is invaluable :) As my understanding of primary sources expanded, I moved away from 1180-1200 towards 1250-1280, to accommodate more heraldic embellishments (ailettes, torse/mantles, etc).
My mail is flat, riveted and galvanized. I'll need to double check the diameter. It came from an Indian seller called AllBestStuff. I've had it for almost 5 years and it has held up well to punishment, although I want to refine it and tailor it. My first job on the coif is to create a flat top, followed by squaring off the bib.
There are several primary examples of flat-topped coifs, mainly effigies. A sculpture from Wells Cathedral depicts what looks like a flat-topped coif. There are six entries for flat-topped coifs on Effigies & Brasses, although others exist. I have found no illuminated depictions so far.
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Effigy of William Longespée c.1226 - © Copyright Philip Halling
My inspiration came from the movie Ivanhoe (1953), starring Robert Taylor. He is depicted with a flat-topped coif, presumably wearing a pot shaped cervelliere underneath.

Ivanhoe before his duel with Sir Brian Bois-Gilbert.
I have found French discussion forums where they suggest the flat-topped coif was achieved using a 'tortilla' (a gamboised torse, as used for helm ornamentation) or a mortar (a cervelliere). I decided to use the lid of a frying pan to construct a 'test' cervelliere.
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Test Cervelliere, with and without coif.
I know it looks as though it's sitting high on my head, but my head is actually touching the top of it. I do have a big forehead :p It was slightly too wide to fit my great helm over, so the real cervelliere will have a lesser circumference. Depending on the materials I have at hand, it will be either stainless steel, aluminum, or brass. Since it's purely aesthetic, I'm not fussed. As you can see, the face opening and bib need tailoring.
Progress photos to come! Any thoughts or suggestions are welcome!