After spending hours researching, I found no information regarding the "Not enough space available" error when trying to transfer files to the hard drive (I'm using a 250gb internal one btw). I was about to just call it quits until I noticed something odd: Xport showed that 512mb of memory had been used on Partition 3, and that 0 space was available. At that moment I remembered I had set aside 512mb for Cloud Storage, which then led to the solution...
For anyone having issues with Xport saying "Not enough free space" or whatever, make sure you have disabled Cloud Storage on your Xbox 360. To do this, go to the Memory Management screen in System Settings, highlight Cloud Storage and select "Device Options", then select Disable. If there is anything saved in Cloud Storage, you have to move/delete it before you can disable it.
Once I did that, everything went fine. Just purchased this game earlier this week for the first time, so now I've got to go enjoy some updated rosters