Okay let me see if I can help you out. First off, what type of produce are you looking for? Yeah the supermarkets are overpriced, but hell you didn't even mention Trader Joe's, Whole Foods, Bristol Farms, Gelsons or the other insanely overpriced trendy markets.
The cost of groceries is crazy high out here just like any other major city, just part of the price you pay to live here, New York, London, etc.
I don't know which farmer's markets you go to, but the ones in the upscale areas are going to be pricy, but you can still get good deals. The Santa Monica, Beverly Hills, Westwood etc. farmer's markets are pricy indeed, but still you can find some vendors at these that are reasonable (at least for LA), and better priced than most supermarkets.
If you want really cheap groceries, you have to go to the ethnic stores. Go to the Hispanic supermarkets, or the middle eastern ones.
Try Jon's Supermarkets for one. There are a couple in Hollywood, Glendale, etc. Also, if you're willing to drive to Echo Park/southeast Glendale, try King Market. It's on San Fernando Road a little bit east of the 2 FWY.
Or Food For Less Supermarkets or other discount supermarkets. But most of these are in the more ghetto areas. And most have lower quality produce, meats, etc. You're getting what you pay for.