How do I upload huge files across the internet without using P2P?

Talk to IT at the office. You've got a legitimate business need (I'm assuming -- if this is your MP3 collection you're on your own ;-) ), they should be willing to work with you on a viable solution. Maybe that will be raising your FTP limit, setting you up with SSH access, or something completely different.

in case this is on Linux, this is very easy:

Use rsync over SSH in a screen session to move the files:

rsync -aPvzl media/ my.home.ip:destination_folder

Start this in a screen session, so you can attach to it while at home.

Possibly use a file splitter and joiner.

Split it into smaller chunks and use the free services, then piece it together.

Personally I would just physically mail it.