Pinworms, you are able to start it fresh again as a BLM. The quest just resets if you abandon it during any of the step, it gets zeroed.

You just need to talk to the smithy, go get the item, buy the weapon, meld it and so on. All it does is cost you time and money if you abandon it halway through. But you can always start over from the first quest in the line. If you cant then you need to contact in-game support or something and make sure you dont have it on another class.