Do you have the /media/ed directory? I know you said you do but please check for spelling and permissions (is the owner root?).

I would personally not mount anything under /media manually myself, that's udev's domain. I would mount it under /mnt or even /tmp. But that's just my paranoia, I have no real arguments why that should not work.

Otherwise your method looks OK (read: exactly what I would have done). But you may expereince the device rebooting halfway through the copying due to cp taking too much CPU time and the watchdog kicking in (trust me, it has happened to me). You can eliminate that by reducing the cp priority with nice.