Garden update: after spreading ant killer over the rest of the yard, the ants - those that remain - are trying to take up residence in the garden itself.
I bought Orange Guard, which is an organic/garden-safe ant killer/repellent. I've discovered that it does kill some ants, but not all of them. The rest simply move away. They don't like Orange Guard's residue.
Once they're away from the plants themselves, I pour boiling water on the ant hill, and that kills them in a non-toxic way. The boiling water would, of course, kill the plants, so using Orange Guard to send them to the garden's edge allows me to kill the others safely.
Gardening is pretty much daily work, doing this. But it's worth it. My tomatoes are over the size of a quarter now and the peas are about to bloom.