Shares are simply the root folders on each drive, so you are really just renaming the paths into a new root folder, no need to move the bits to a new physical location.
in mc, navigate to /mnt/disk1 in the left and right pane, in the right pane Mkdir data, then navigate into the data folder. In the left pane select shares you want to move into "data", then RenMov them. Should happen very quickly.
Repeat for /mnt/disk2 in the left and right pane, then /mnt/disk3, etc, etc. If the shares in question use pools, do the same thing using /mnt/poolname.
STAY OUT OF /mnt/user while playing around with mc if you are working with /mnt/diskX or /mnt/poolname. If you want to work in /mnt/user, make sure BOTH PANES are in /mnt/user, never mix the two.
You will need to change the host paths on each and every effected container, adding "data" into their paths, i.e. if the original host path was /mnt/user/movies, the new path would be /mnt/user/data/movies