You're going to get a ton of skepticism, but I think it's possible in a dense area to find enough people who have enough overlap in the staples they consume who are willing to pay for this. I would try to focus on quality first, proving that you can get super high customer retention and unit margin, before trying to be cost-competitive with a larger grocer.
I am involved with a company called Teamshares that helps small businesses convert to employee ownership. A big part of what makes it work is exposing company financials to all employees in a way that helps connect one's actions with financial performance.