Thank you all for all of your help! I decided to go with some pin badges from the official Discworld merchandise site. I'm going to have to finagle a backing to make them secure on the vest, (one already fell off in his proud scampering around the house) but Carrot's initial look is pretty awesome I think! The City Watch badge pin looks smaller than I had hoped, even though I measured, but all in all, I'm happy! It was hard to narrow down choices once I went with this direction.

https://cdn.masto.host/writing/media_attachments/files/111/053/618/298/836/775/original/0ea8337352178c9d.png

https://cdn.masto.host/writing/media_attachments/files/111/053/619/716/058/873/original/da9ad17dd3cef3f6.png

https://cdn.masto.host/writing/media_attachments/files/111/053/620/930/061/094/original/7edf7dfdc3a36452.png