KYA! Thank you everyone! I finally managed to cue this quest. Though I did have one rather unusual thing happen- according to my tally, I played a total of fifty games before it agreed to run O_O. Well, stranger things have happened in Final Fantasy games I'm sure (and these were with 10+ different characters, incidentally).

I am now the VERY proud owner of a Carbunkle card.

Now, to chase down that Doctor Kadowaki...

PS- I've also found joker and relieved him of his Leviathan card.