Some ants like sugar some like protein. You gotta kill the queen, any other action is temporary.
This winter I had rats in the garage, on the menu, fire ant killer. Pretty sure the rats didn't even get indigestion. The point being, as a rule, Ant poisons made today are extremely low toxicity, just enough to kill an ant. One meal can kill an ant, think about what size of that meal is to you, less than the head of a pin.
I'm not a fan of chemicals but I will drop queen-killing baits in a heartbeat. A bonus is that you can localize your attacks to the mounds, you can still end up playing whack-a-mole on the mounds.
Queen killing baits (slow acting) can take longer but they can deliver the coup-de-grace.
I wouldn't broadcast spread unless the infestation was real bad.
The university of Arkansas has some decent information on fire ant control.
http://www.uaex.edu/publications/pdf/fsa-7036.pdfhttps://www.uaex.edu/publications/pdf/FSA-7052.pdf