Promote the ability to grow some kind of food that's unusual enough to tell your friends about. If, for example, I were able to harvest fresh heirloom tomatoes in Maine in January and feed them to my dinner guests, that would be both good for my ego and good for your marketing. A more realistic example, perhaps, is the fad for backyard chickens: Raising chickens is fun because, every time you serve someone an omelet or a quiche, you get to start a conversation about the chickens. And the eggs make great gifts. Play up the odd and potentially fashionable.
Is there something particularly tasty that your system is uniquely good at growing? Is there something particularly hard to grow that your system makes easier?
Are the plants fun to look at? Would you show the garden to your friends?
Can kids run it? Perhaps it's an educational experience. Pitch it to school groups, community centers, local parks, science museums, children's museums, et cetera.
Can one start small and grow into a full system? "Feed your whole family on a 20-by-20-foot lot" is actually not such a great sales pitch. You ask for too much commitment. I've tried hobbies before. Most of them don't last and I end up selling the starter kit on Craigslist three years later. Worse, if you convince me that replacing 100% of my grocery bill is the victory condition, when I only manage to replace 37% of my grocery bill I will feel like a failure, which is just perverse. What you want, instead, is for me to successfully grow four plants, swell with pride, and tell all my friends that gardening is awesome.
So a better pitch IMHO would be "try this thing on a small garden and enjoy the nice fresh [insert delicious thing here]; then, if you like it, you can expand it bit by bit, until you wake up one year and find that your 20-by-20 foot garden is producing more food than your family of four can eat in a year, with almost no effort and at a cost of pennies a day."
Congratulations on being smart and realistic enough to try and find your market before you invest any more time or money. Good luck!
EDIT: Ooh, here's a fun one: Take a hint from the local county fair and gamify this. Build a social network. Turn it into a competition to see who can grow the most pounds of food in a given area, or something. It's like Farmville with real farms.
I like the exotic angle. One suggestion from an aquaponics guy that I came across (the AutoMicroFarm products would be aquaponics systems) is to grow some kind of an exotic fish that can be sold to asian communities for thousands of dollars. As far as plants, perhaps something lesser-known tropical that would do well in a controlled environment?
We're totally not typical in that we garden to save money and have good foo, and we aren't shy about saving money (couponing, etc.).
But, let me point out that--in addition to the motivation being possibly misguided, there's the other elephant in the room: customers worried about saving money on staple foods often have way less money than those who have other motivations.
Perhaps you can try an angle that's not vanity, and not frugality, but more taste and convenience. Yeah, you wouldn't think of a garden as convenient, but it's actually really cool to just step outside and grab some lettuce for the salad, or some fruit, etc. Also, I can't overstate how much better (usually) our homegrown food tastes. And of course, there's probably some psychology in there that helps convince me since I grew it myself. Use that to your advantage. Don't forget how evocative taste and smell is; how easily these senses can be linked to feelings and memories.
Think about how Harley-Davidson position their bikes. They don't say, "Hey, here's a way to get around" — instead, their positioning is more along the lines of "ZOMG it's a Harley! How COOL would you look driving this thing, huh?" They're primarily checking off the "Feel like James Dean" box on their customers' wishlists, not the "transportation" box.
Similarly, an easy-home-gardening product is checking the "Feel good about yourself" box, not the "nutrition" box. The nutrition is just a nice gimme. So in that way it doesn't make sense to position it against grocery stores. Most grocery stores are not selling "Feel good about yourself." (A few are, like Whole Foods, but they're also way more expensive than the normal ones, and they also don't make a big deal about the price comparison, because those other guys aren't selling moral superiority at all.)