Alright; 13 gb of files on ServerA needs to move to ServerB.
* I have root to ServerA, but have to operate in a jail-shell on ServerB.
* The 13gb of files are spread through 4 directories and about 10k files.
* I need to move them into the jail-shell on ServerB, inside a folder writable by the user I'll be using. The directory/file-tree structure needs to remain intact (i.e. the four folders get moved, and have identical contents as the original).
* If it matters, it's mostly multi-media (mp*).
* I cannot transfer the files to the computer I am on, they have to go directly server to server.

Do we have any good ideas on how to do this on a 'run command, walk away, return next day' basis?

Depending on structure, scp -r is quite good. The sftp utility is good for this as well. There is also tar, though that requires being able to untar it on the other side.

Worst case, you can create a perl script that will push them across, though it's not likely to be needed. SCP/SFTP would be the best case, really.