I'm not sure about the consequences of rats eating the ants but I think I may have a bright (very unusual) idea that worked for my stepmom in the states.
When I went to visit her, I was really shocked by this mass infestation of ants that were crawling everywhere in her kitchen. I mean, they were all over her counters and in the cupboards, I mean everywhere. I said, oh my God how on earth are you going to deal with them without killing them or putting down some kind of poison? The infestation was freaky but I didn't want the ants to die, so she said 'oh, their bowl is empty is all. Watch this'
She got out the maple syrup and filled up a little bowl on the corner. To my amazement, the next day there wasn't a trace of an ant anywhere. They were all feeding out of this little bowl completely out of site lol It was really funny and pretty cute.
Maybe you should try it? You could put down a little bowl of syrup or something sugary, keep it topped up away from the cage and the ants won't go anywhere near the cage. Sounds ridiculous, but it really works.