How do I export banshee library settings to another machine?

The Banshee configurations are stored in the ~/.config/banshee-1/ directory. Those configurations can be found in the ~/.config/banshee-1/banshee.db (if you have the sqlite3 tool you can take a look inside this file).

I don't know if there are significant differences in the format of the files from one version to another, but I suggest that you save the entire directory and try to restore it after downgrade.

Update:

A more safe option to keep bashee settings is using the sqlite3 command:

$ sudo apt-get install sqlite3
$ cd ~/.config/banshee-1
$ sqlite3 banshee.db ".dump" > BACKUP_FILE

After the downgrade you can restore the file (first copy the backup file to the ~/.config/banshee-1 directory):

$ cd ~/.config/banshee-1
$ cat BACKUP_FILE | sqlite3 banshee.db