Lostbears is correct.
you'll have to go back and address the way EAC is storing or issuing the database, folder and file paths it outputs.
It's a bit confusing but there are options listed online in EAC forums and tutorials. Google for EAC info, tutorials, actually I've posted links to some here on the 'gon, already.
here's another:
http://www.anythingbutipod.com/forum/showthread.php?t=52398
there are a few topics listed in this forum near the top of the page which should answer your concerns.
The way I use EAC is to output to genres right onto the C drive. Thereafter I copy and paste them into a NAS drive all my machines can see, and backup those by copying and pasting them into a USB drive I use for back up only. It's an identical folder tree as the NAS drive. Then I unplug the USB drive until it's time to back up again.
I also maintain my music by Artist > album for my active music library.
EAC will set what ID tag info you select. track #, file name, genre, date, etc.
it'sd not to hard to change how EAC outputs files, just look around a bit more if the above link doesn't help..
Good luck.