Well, we finally seem to have got rid of most of the ants. It took a lot of patience, and we had to try a few different tactics. We first used some of the commercial “ant killer” products sold in stores, but none of them worked.
Instead we first tried applying a daily solution of borax and sugar/honey. The ants take this back to the queen and eventually it is supposed to kill the colony. (Incidentally, for the first time ever, we had an invasion of little black ants in our house and this method worked to get rid of them within a few days.) See How to Kill Ants with Borax - A Deadly Ant Killer Recipe for more information.
Although the ant mounds were getting smaller with the the application of the daily borax solution, things were moving a bit too slowly outside for us with so we decided to switch tactics. We shovelled the top of the ant mound into a large plastic container of warm water and soap. The ants move quickly and bite so we used gloves and rubber boots with tanglefoot half way up. We then soaked what was left with a mixture of hot water, borax and soap.
This seems to have done the trick. Some ants have tried to relocate and start up new colonies, but they are easy to deal with since we catch them when they are small.