Dragoon quest broken, how do I progress?

I broke the level 45 dragoon quest. It's the exact same issue as this bug report. One additional detail, I had exactly 4 open slots in my inventory when I tried to turn it in. The poster of the bug report didn't mention the status of their inventory but I think that has something to do with it. I'd love to add that detail but bug reports are locked and they don't seem to want duplicates.

Anyway, the details are all the same. I got my helmet, the quest items are gone, I can't turn it in, and I can't abandon it. Now what? I'm leveling dragoon for the story but I can't complete the quest. Can this be fixed somehow? I don't care about the i90 wyrm gear. I was going to turn it into GC seals anyway. I just want the next quest to be accessible.