I beat them! It was absolutely glorious!
They captured one of my colonies before leaving and crossing their territory to attack my federation allies. So... what happened to feeding on my babies as promised? I went after them into their turf, split my fleet into two 80k and placed them on either flank of the hyper space exit within range of where they would drop out of hyperspace. I also built a fortress within range and placed a third fleet of torpedo corvettes 3k fleet power where the AE would arrive.
They waltzed right into my trap and it went better than I dared to hope. Honestly I don't think the corvette's did any damage. I think the main advantage is flanking them from both sides. It's the second time I've successfully attacked the flank or rear and it definitely makes a big difference.