Got a fishing retainer? That's the only thing I can think of - send them out for a fish you would rather not catch. Collect a bunch of them and then start desynthing away.

Alternatively, spend 3k gil each on the item over in the Silver Bazaar, that is used for the Zodiac quest. Desynth that and level up a ways on it. Not too sure that you can recoup your cost on it anymore though.