Long story short: I made three different insignia I didn’t have on the coats yet, then three of each of the two types of cotton coat materials. I then created the first two cotton coats with a different insignia… but then I was unable to create a third one? It says I need Tailoring skill 150 to use the cotton, but my skill is 174? And again, the first two went fine, but then it just stopped.
I have tried relogging and restarting the game, but neither of that helped.
EDIT: I made it to Tailor 175, and now I can craft the coats again. Strange.