I wonder if you got some sort of karaoke machine and cranked up the volume whether that would amplify your voice louder so that she could hear you and fly to the sound. I don't know if she would hear electronic distortion or not, but if birds can recognize a voice over skype/face-time/the phone, I am guessing she would still be able to tell it was you through the mic/speakers.
I used to put a karaoke machine in my open window and turn the volume up. People could hear it all the way across the street without any effort on my part...Mine was used as part of a prank, but I'm thinking this idea could work for you with the right speakers.
A drone is another possibility, but that could get expensive/complicated...