There are many products on the market that are labeled for use in vegetable gardens. Several are labeled as acceptable for certified organic gardens. You'll want to use baits for your purpose, rather than the mound drenches.

Just Google 'organic fire ant baits ' and visit the edu sites. Stay away from the home remedy stuff. It doesn't work.

Texas A & M people have done a lot of research on Fire Ants and their control and most all .edu sites with information about Fire Ants uses them as a resource. Fire Ant control is not something that can happen in the short term, it does require a long time.

Here is a link that might be useful: Fire Ant information

I have more trouble attracting ants with a compost pile than with smother/lasagna/sheet mulching using the same 'ingredients.' This new bed hasn't had any issues with ants. They seem to occupy arbitrary spots in grass or beds, with whatever gardening I do having no effect unless I make a real compost pile. There's cardboard on the bottom, topped with leaves, grass, some peanut shells, plant trimmings, kitchen scraps. The smother's been there all summer, just added the Cycads about a week ago, the Glads a while back in a spot where the grass was already dead when I started.