I wouldn't worry about the ants and I really wouldn't use any poisons. I would avoid putting any fruit in there since this will attract ants. I know here in the U.S. mourning doves will actually sit over an ant hill and let the ants crawl on them and I have seen them do this but for the life of me I can't remember why...
Maybe plant some bird safe plants that they could chew on? Even some veggies in pots and maybe hang them from the side so they could just eat them out of there. I don't know anything about Alexandrines or GCC's so I'm just saying what I had thought about for my birds. Also a lot of food hidden in areas so they could forage
