Uhhh ... thought I did address:
"I know in pre-Moodle 2.x, you could just stick the file in the local
uploads folder and restore it from there, but with Moodle 2.X, I have no
clue."
In 2.x moodlese that's a file system repository. On a localhost machine, one could drag and drop that large backup in the file system repository directory created and linked in whatever 2.x version of Moodle you are running to skirt the upload issue.
Only difference in localhost from production server out on the net ... one may not be able to do drag and drop in operating system sense but use FTP/WinSCP, etc. 'drag and drop' to xfer the large backup to the file system repository manually created and linked to in production Moodle.
Sorry ... other than tweaking apache/php to allow larger and larger uploads via Moodle UI, file system repo is the only other alternative. It is also faster and less prone to timeouts, other issues (apache/php).
Also ... since this has happened once on the production server, think you will run across it again ... courses only grow they do NOT shrink (if using just Moodle file system for storing files). So think taking a local host approach is only delaying what you'll eventually end up doing on the production server. 
Sometimes an 'easy button' just doesn't exist! :|
OR ... one could make a backup of the course only this time deslecting say 1/2 of the mp3/audio links. Save the backup with added text in file name - bu1 (backup 1).
Then make another backup, this time de-selecting the stuff you backed up in bu1 and selecting only the items not included in bu1. Save the backup with bu2 in the name.
Restore bu1 to a course. Then restore bu2 to the existing course.
When you do the second restore, don't expect everything to come back into the course in the same section/week, whatever as the original course. You will have some re-arranging to do.
To me ... that could be more work than file system repo setup.
'spirit of sharing', Ken