I too will suggest robocopy. The newest version from Microsoft (included with Windows 7) is multithreaded which is great for massive amounts of data. I would suggest a process something like this:
Environment: NetApp called toaster with multiple shares. Server called microwave.
Document share permissions on toaster by looking at them in Windows Explorer
Build a baseline
Create multiple shares on microwave with the same names as the ones on toaster
Run robocopy \\toaster\share1 \\microwave\share1 /copyall /mir /r:0 /w:0 /log:robolog.txt in a command prompt
Repeat for each additional share.
Review robolog.txt to see how many files were missed (especially the very bottom) and troubleshoot
Get an outage window
Run robocopy \\toaster\share1 \\microwave\share1 /copyall /mir /r:0 /w:0 /log:robolog.txt in a command prompt
Repeat for each additional share. This will only copy the changed data which will reduce the outage duration.
Repeat for each additional share
Review robolog.txt to see how many files were missed (especially the very bottom) and troubleshoot
Shutdown toaster
Rename microwave to toaster
There are a lot of different tweaks depending on your tolerance for downtime, need for speed and number of shares, but this should get the data off the NetApp. Play with robocopy a bit to get the hang of it.
Final step: Keep toaster in the lab and find out why people adore them.