That's funny! It was working before, and although I went to Typekit website to republish the kits and make sure the code provided by them was Ok, something wasn't working after all.
The way I added my fonts was also given by @Daniel in the Community but for some reason this other way works while the other stopped working 
So I give you, and all, many thanks for your help.
I now encountered a different problem with the export script I'm using to add a 1px border but I'll follow up in its own topic.