In 1974 the fire ants were no further North in Mississippi than Meridian, Ms. That year, EPA made the claim that Myrex was environmentally unsafe and Myrex’ sole purpose was to kill fire ants and was effective. I noticed that mounds were further North about 50 miles each year after Myrex was outlawed. In 1985 was the first time I noted mounds on the Tennessee/Mississippi state line. The expansion of the fire ant territory can be attributed to EPA’s removing Myrex from the armamentarium of ant poisons.
I imagine that a good way to get rid of a fire ant colony would be to spade deeply around the exposed mound slightly raising it and then saturating the exposed underside with a combination of wasp spray and liquid ammonia. I never tried it because that would be using the products in a manner inconsistent with their labeling and that would be a violation of federal law.
I would also have to surmise in my best guess that it would leave a brown spot in the lawn where grass wouldn't grow for probably 2-3 years, but that is just a guess since I would never try it, but I'd bet if I did it would pretty effectively kill off the entire colony.
Just an untried hypothesis.