eureka!

The Garageband export problem is solved!

Somebody (shout out to ronkurz at the Apple Support forums) has received an answer from a helpful Apple Store employee. Apparently all my problems have been caused by having forward slashes (/) in my filenames! For the non unix-types out there, the forward slash demarcates a filepath. When iTunes attempted to import the mixdown from Garageband it got all confused by the forward slashes and when 'HUH WHAT THE HUH NAH I'LL DISCARD THAT' and dissolved the file off into the ether.
Whaddya know. Exports work just fine now.

I feel kinda stupid. But hey! Who woulda thunk?