I think you could use an ssh tunnel between the intermediary and the destination such that the scp connection from the source makes it all the way through in one go, rather than leaving files on the intermediary. You'd be forwarding to the ssh port via ssh, so it would be a confusing bit of sshception.

If I tried to actually come up with the actual commands for this, I'm sure I'd burn a whole afternoon on fiddling with it.