I played the harmony to this tune as I was figuring it out at a party last night.
I'm pleased to have figured out a (slightly) better way of recording myself. I've had the problem that if I listen on headphones to the melody while I record the harmony, the tracks aren't quite aligned. I discovered by accident that if I play the melody out loud on my computer speakers while recording the harmony, the computer microphone will pick up both parts. Obviously this decreases the sound quality a little but, but I'm ok with that. I also find it easier to hear the mix of the harmony and melody notes when the melody is out-loud, but I'm not sure if there's a real difference in terms of the sound recorded or not.