Have you given Aldi a try?
Please keep in mind that I LOVE Publix--I'm not knocking the chain. Publix has fabulous sale prices, a great selection and the best customer service around. And Aldi is great, but they don't have a wide variety of foods, so if you need more specialized items you have to pick them up elsewhere.
This post is purely motivated by my desire to share options for saving on your grocery bill--it's not endorsed or sponsored by Aldi in any way!