This is not an organic solution, but Orthene dust applied at the rate of 1 Tablespoon per mound works quickly. It also smells horrible so store it outside of the house.
I definitely agree with the non chemical approach and am looking forward to any good ideas for fire ants. The non biting ants are welcome to stay. My chickens do a pretty good job with the back yard. Maybe I will revive the chicken tractor to keep them safe from neighborhood dogs in front!
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