Well the disk space is simply a USB drive plugged into the router.
But if you feel it really should have GB of RAM (??) then a bigger box will likely be needed. And the USB routers don't tend to have the fastest I/O paths, either.

ISTR that there are a few "router" distros for Linux with nice web GUIs. I wonder if one of those, but on a small Atom or AMD box, would have a good enough web setup to make this as easy as a DDWRT router?

Actually, google search seems to suggest there might be some nice "NAS Linux" distros, too.
Eg. http://www.openfiler.com

I have no experience with those, preferring to roll my own, but something like that might be best for your requirements.

Cheers