I just want to add to the existing answers something that might improve your transfer once you've got your hard drive connected to a server with good bandwidth.
I needed to transfer large amounts of data several times between two web servers and instead of using common FTP or WGET commands to upload or download the data, I have been using the Linux SCP command. You can find more info here:
You will need SSH access to both servers and then you can copy one file, or many files recursively.
So, if you only have large files instead of many small ones, I think it will copy fast enough.
At a transfer rate of 11MB/second between servers the transfer would last about 25 hours.
Good luck! ;)