I'd focus on a few major markets and work hard to get as many menus up as possible. People are always looking for free advertisements and having their menu online is one form. I'd push that as much as possible. Since this is your full time effort, you may need to spend money on marketing to get the ball rolling. Perhaps enter the menu's yourself (or hire a VA to do it) and then drop the restaurant a note saying that their menu is now online and they can make changes at this website for free.
Other ideas, perhaps white label it to newspapers and/or city websites? In San Diego, there is a dining guide section at signonsandiego.com and this would fit into what they are doing. They also have someone who is doing reviews weekly, which could now include populating the full menu.