The magic of the power-down-everything-and-reboot seems to have found the Itunes Server.
@stretch, thanks for the suggestion — I had already tried downloading the client and hit the same wall, and your posting pointed me at the above “solution”.
Interestingly, for those who follow this thread in the future, it appears that Firefly had crashed, although FrontView (the ReadyNAS admin utility) was reporting it as healthy.
I’ll post again once I’ve discerned that everything really is solid.