I've worried about this as well. Thankfully I also won a rank 4 on my main character like Kristal ... and so Black Belt item was my choice, but what if I won it on a mule? What would I do? It really limits my choices of what to pick and I'm not quite sure that's fair. I don't think SE's intent was that you could get 10 marbles and that was it, I'm sure they considered mules since level 5 is the requirement, isn't it?
If Mog Balls were deliverable to any character within the same account, that should be as sufficient of a solution as I could hope for from SE.
Please have the devs change this! This is a flaw in the system imo.
Did I mention that the devs were very awesome, super incredible, masters of all moogles? :p