To make ants (somewhat voluntarily) move from one home to another, ant keepers shine bright lights into the old home, and leave the new home cool and inviting. I wonder what would happen if you put the hottest spot light that you have, right up to the place where they come into the house? Would a few days "train your ants?!"
They also use a baby powder/water solution to use on the walls of terrariums so the ants can't climb up and out. Maybe given the orientation of your invaders, this would be helpful too?
Hmmm bright lights! That is illuminating!